2017
12
2
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165
On (Semi-) Edge-primality of Graphs
2
2
Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an edge-prime (or a semi-edge-prime) labeling is called an edge-prime (or a semi-edge-prime) graph. In this paper we determine the necessary and/or sufficient condition for the existence of (semi-) edge-primality of many family of graphs.
1
14
W.-C.
Shiu
W.-C.
Shiu
Hong Kong Baptist University
China
wcshiu@hkbu.edu.hk
G.-C.
Lau
G.-C.
Lau
Universiti Teknologi MARA （Segamat Campus)
Malaysia
geeclau@yahoo.com
S.-M.
Lee
S.-M.
Lee
Retired Prof of San Jose State University
USA
sinminlee@gmail.com
Prime labeling
Edge-prime labeling
Semi-Edge-prime labeling
Bipartite graphs
Tripartite graphs.
[1. J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, New York, MacMillan, 1976.##2. T. Deretsky, S.M. Lee, J. Mitchem, On Vertex Prime Labelings of Graphs, Graph Theory, Combinatorics and Applications, 1, (1991), 359-369.##3. F. Harary, R. Guy, On the M¨obius Ladders, Canad. Math. Bull., 10, (1967), 493-496.##4. P. Haxell, O. Pikhurko, A. Taraz, Primality of Trees, J. Combinatorics, 2, (2011), 481- 500. ##5. J.A. Gallian, A Dynamic Survey of Graph Labeling, Electronic J. Comb., (2016), #DS6. ##6. E. Salehi, Integer-magic Spectra of Cycle Related Graphs, Iranian Journal of Mathematical Sciences and Informatics, 1(2), (2006), 53-63.##7. M.A. Seoud, M.Z. Youssef, On Prime Labelings of Graphs, Congr. Numer., 141, (1999), 203-215. ##8. A. Tout, A.N. Dabboucy, K. Howalla, Prime Labeling of Graphs, Nat. Acad. Sci. Letters, 11, (1982), 365-368.##9. M. T. Varela, On Barycentric-Magic Graphs, Iranian Journal of Mathematical Sciences and Informatics, 10(1), (2015), 121-129.## ##]
A Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
2
2
In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first linearize the equation using quasilinearization technique and the resulting problem is solved by a third degree B-spline function. Some numerical examples are included to demonstrate the feasibility and the efficiency of the proposed technique. The method is easy to implement and produces accurate results. The numerical results are also found to be in good agreement with the exact solutions.
15
34
Z.
Parsaeitabar
Z.
Parsaeitabar
Shahrood University
Iran
parsaee.z@gmail.com
A. R.
Nazemi
A. R.
Nazemi
Shahrood University
Iran
nazemi20042003@yahoo.com
B-spline
Collocation method
Lane--Emden equation
Singular IVPs.
[1.J. M. Ahlberg, E. N. Nilson, J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, NewYork, 1967. ##2. A. Aslanov, A Generalization of the Lane-Emden Equation, International Journal of Computer Mathematics, 85, (2008), 1709-1725.##3. A. Aslanov, Determination of Convergence Intervals of the Series Solutions of EmdenFowler Equations Using Polytropes and Isothermal Spheres, Physics Letters A, 372, (2008), 3555-3561.##4. A.S. Bataineh, M.S. M. Noorani, I. Hashim, Homotopy Analysis Method for Singular IVPs of Emden-Fowler Type, Communications in Nonlinear Science and Numerical Simulation, 14, (2009), 1121-1131.##5. C. M. Bender, K.A. Milton, S.S. Pinsky, Jr.L.M. Simmons, A new Perturbative Approach to Nonlinear Problems, Journal of Mathematical Physics, 30, (1989), 1447- 1455.##6. R. Bellman, R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965.##7. K. Boubaker, R.A. Van Gorder, Application of the BPES to Lane-Emden Equations Governing Polytropic and Isothermal Gas Spheres, New Astronomy, 17, (2012), 565-569.##8. N. Caglar, H. Caglar, B-spline Solution of Singular Boundary Value Problems, Applied Mathematics and Computation, 182, (2006), 1509–1513.##9. M.S.H. Chowdhury, I. Hashim, Solutions of Emden-Fowler Equations by Homotopy Perturbation Method, Nonlinear Analysis: Real World Applications, 10, (2009), 104-115.##10. M.S.H. Chowdhury, I. Hashim, Solutions of a Class of Singular Second-order IVPs by Homotopy-Perturbation Method, Physics Letters A, 365, (2007), 439-447.##11. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York, 1962.##12. C. de Boor, A practical Guide to Splines, Springer-Verlag; 1978.##13. M. Dehghan, M. Shakourifar, A. Hamidi, The Solution of Linear and Nonlinear Systems of Volterra Functional Equations Using AdomianPade technique, Chaos, Solitons and Fractals, 39, (2009), 2509-2521.##14. M. Dehghan, A. Hamidi, M. Shakourifar, The Solution of Coupled Burgers Equations Using AdomianPade Technique, Appled Mathematics and Computation, 189, (2007), 1034–1047.##15. M. Dehghan, F. Shakeri, The Use of the Decomposition Procedure of Adomian for Solving a Delay Differential Equation Arising in Electrodynamics, Physica Scripta, 78, (2008), 1–11, Article No. 065004. ##16. M. Dehghan, M. Tatari, The Use of Adomian Decomposition Method for Solving Problems in Calculus of Variations, Mathematical Problems in Engineering, 2006, (2006), 1-12. ##17. M. Dehghan, J. Manafian, A. Saadatmandi, Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method, Numerical Methods for Partial Differential Equations, 26, (2010), 448–479.##18. M. Dehghan, F. Shakeri, Use of He’s Homotpy Perturbation Method for Solving a Partial Differential Equation Arising in Modeling of Flow in Porous Media, Journal of Porous Media, 11, (2008), 765778.##19. M. Dehghan, F. Shakeri, Approximate Solution of a Differential Equation Arising in Astrophysics Using the Variational Iteration Method, New Astron, 13, (2008), 53-59.##20. M. Dehghan, F. Shakeri, Use of He’s Homotopy Perturbation Method for Solving a Partial Differential Equation Arising in Modeling of Flow in Porous Media, Journal of Porous Media, 11, (2008), 765-778.##21. M. Dehghan, A. Saadatmandi, Variational Iteration Method for Solving the Wave Equation Subject to an Integral Conservation Condition, Chaos, Solitons and Fractals, 41, (2009), 1448-1453.##22. J. H. He, Variational Approach to the Lane-Emden Equation, Applied Mathematics and Computation, 143, (2003), 539-541.##23. M. Kadalbajoo, V. Kumar, B-spline Method for a Class of Singular Two-point Boundary Value Problems Using Optimal Grid, Applied Mathematics and Computation, 188, (2007), 1856–1869.##24. A. H. Kara, F. M. Mahomed, Equivalent Lagrangians and Solutions of Some Classes of Nonlinear Equations, International Journal of Non–Linear Mechanics, 27, (1992), 919–927. ##25. A. H. Kara, F. M. Mahomed, A Note on the Solutions of the Emden Fowler Equation, International Journal of Non-Linear Mechanics, 28, (1993), 379–384.##26. M. Lakestani, M. Dehghan, Four Techniques Based on the B-spline Expansion and the Collocation Approach for the Numerical Solution of the Lane-Emden Equation, Mathematical Methods in the Applied Sciences, 36(16), (2013) 2243-2253.##27. S. Liao, A New Analytic Algorithm of Lane-Emden Type Equations, Appled Mathematics and Computation, 142, (2003), 1-16.##28. V. B. Mandelzweig, F. Tabakin, Quasilinearization Approach to Nonlinear Problems in Physics with Application to Nonlinear ODEs, Computer Physics Communications, 141, (2001), 268-281.##29. H. R. Marzban, H. R. Tabrizidooz, M. Razzaghi, Hybrid Functions for Nonlinear Initialvalue Problems with Applications to Lane-Emden Type Equations, Physics Letters A,372, (2008), 5883–5886.##30. G. Micula, Handbook of Splines, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.##31. R. Mohammadzadeh, M. Lakestani, M. Dehghan, Collocation Method for the Numerical Solutions of Lane-Emden Type Equations Using Cubic Hermite Spline Functions, Mathematical Methods in the Applied Sciences, 37(9), (2014), 1303-1717.##32. K. Parand, M. Razzaghi, Rational Chebyshev tau Method for Solving Higher-order Ordinary Differential Equations, International Journal of Computer Mathematics, 81, (2004), 73-80.##33. K. Parand, M. Razzaghi, Rational Legendre Approximation for Solving Some Physical Problems on Semi-infinite Intervals, Physica Scripta, 69, (2004), 353-357.##34. K. Parand, M. Shahini, M. Dehghan, Rational Legendre pseudospectral Approach for Solving Nonlinear Differential Equations of Lane-mden Type, Journal of Computational Physics, 228, (2009), 8830-8840.##35. K. Parand, M. Dehghan, A. R. Rezaei, S. M. Ghaderi, An Approximation Algorithm for the Solution of the Nonlinear LaneEmden Type Equations Arising in Astrophysics Using Hermite Functions Collocation Method, Computer Physics Communications, 181, (2010), 1096-1108.##36. P. M. Prenter, Splines and Variational Methods, New York: John Wiley, 1975.##37. A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Springer-Verlag, Berlin, 2007.##38. J. I. Ramos, Linearization Methods in Classical and Quantum Mechanics, Computer Physics Communications, 153, (2003), 199-208.##39. J. I. Ramos, Linearization Techniques for Singular Initial-value Problems of Ordinary Differential Equations, Applied Mathematics and Computation, 161, (2005), 525- 542.##40. J. I. Ramos, Series Approach to the Lane-Emden Equation and Comparison with the Homotopy Perturbation Method, Chaos, Solitons & Fractals, 38, (2008) 400-408.##41. J. I. Ramos, Piecewise-adaptive Decomposition Methods, Chaos, Solitons & Fractals, 40, (2009), 1623-1636.##42. L. L. Schumaker, Spline Functions: Basic Theory, Krieger Publishing Company, Florida, 1981.##43. N. T. Shawagfeh, Nonperturbative Approximate Solution for Lane-Emden equation, Journal of Mathematical Physics, 34, (1993), 4364-4369.##44. F. Shakeri, M. Dehghan, Solution of Delay Differential Equations via a Homotopy Perturbation Method, Mathematical and Computer Modelling, 48, (2008), 486-498.##45. A. Saadatmandi, M. Dehghan, A. Eftekhari, Application of He’s Homotopy Perturbation Method for nonlinear System of Second order Boundary Value Problems, Nonlinear Analysis: Real World Applications, 10, (2009), 1912-1922.##46. O. P. Singh, R. K. Pandey, V. K. Singh, An Analytic Algorithm of Lane- Emden Type Equations Arising in Astrophysics Using Modified Homotopy Analysis Method, Computer Physics Communications, 180, (2009), 1116-1124.##47. M. Tatari, M. Dehghan, On the Convergence of Hes Variational Iteration Method, Journal of Computational and Applied Mathematics, 207, (2007), 121-128.##48. R. A. Van Gorder, An Elegant Perturbation Solution for the Lane-Emden Equation of the Second Kind, New Astronomy, 16, (2011), 65-67.##49. R. A. Van Gorder, Analytical Solutions to a Quasilinear Differential Equation Related to the Lane-Emden Equation of the Second Kind, Celestial Mechanics and Dynamical Astronomy, 109, (2011), 137-145.##50. R. A. Van Gorder and K. Vajravelu, Analytic and Numerical Solutions to the LaneEmden Equation, Physics Letters A, 372, (2008), 6060-6065.##51. A. Wazwaz, A New Algorithm for Solving Differential Equations of Lane- Emden Type, Appled Mathematics and Computation, 118, (2001), 287-310.##52. A. Wazwaz, The Modified Decomposition Method for Analytic Treatment of Differential Equations, Appled Mathematics and Computation, 173, (2006), 165-176.##53. A. Yildirim, T. O zi¸s, Solutions of Singular IVPs of Lane-Emden Type by the Variational Iteration Method, Nonlinear Analysis, Theory, Methods & Applications, 70, (2009), 2480-2484.##54. S. A. Yousefi, Legendre Wavelets Method for Solving Differential Equations of LaneEmden Type, Applied Mathematics and Computation, 181, (2006), 1417-1422.##55. S. Yuzbasi, A Numerical Approach for Solving a Class of the Nonlinear LaneEmden Type Equations Arising in Astrophysics, Mathematical Methods in The Applied Sciences, 34 (18), (2011), 22182230.##56. S. Yuzbasi, A Numerical Approach for Solving the High-order Linear Singular Differentialdifference Equations, Computers and Mathematics with Applications, 62 (5), (2011), 2289-2303.##57. S. Yuzbasi, N. Sahin, Numerical Solution of a Class of Lane-Emden Type Differentialdifference Equations, Journal of Advanced Research in Scientific Computing, 3(3), (2011), 14-29.##58. S. Yuzbasi, M. Sezer, A Collocation Approach to Solve a Class of Lane-Emden Type Equations, Journal Advanced Research in Applied Mathematics, 3(2), (2011), 58-73.##59. B.-Q. Zhang, Q.-B. Wu, X.-G. Luo, Experimentation with Two-step Adomian Decomposition Method to Solve Evolution Models, Applied Mathematics and Computation, 175, (2006), 1495-1502.#### ##]
Ordered Krasner Hyperrings
2
2
In this paper we introduce the concept of Krasner hyperring $(R,+,cdot)$together with a suitable partial order relation $le $.xle y$. Also we consider some Krasner hyperrings and define a binary relation on them such that to become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring $(R,+,cdot,le)$, we obtain an ordered ring. Moreover, we study some properties of ordered Krasner hyperrings.
35
49
S.
Omidi
S.
Omidi
Yazd University
Iran
omidi.saber@yahoo.com
B.
Davvaz
B.
Davvaz
Yazd University
Iran
davvaz@yazd.ac.ir
Algebraic hyperstructure
Ordered ring
Ordered Krasner hyperring
Strongly regular relation
Pseudoorder.
[1. A. Asokkumar, Derivations in Hyperrings and Prime Hyperrings, Iranian Journal of Mathematical Sciences and Informatics, 8(1), (2013), 1-13.##2. F. W. Anderson, Lattice-Ordered Rings of Quotients, Canad. J. Math., 17, (1965), 434-448.##3. M. Bakhshi, R. A. Borzooei, Ordered Polygroups, Ratio Math., 24, (2013), 31-40.##4. P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani editor, Italy, 1993.##5. P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, 5, Kluwer Academic Publishers, Dordrecht, 2003.##6. J. Chvalina, Commutative Hypergroups in the Sence of Marty and Ordered Sets, Proc. Internat. Conf. Olomouck (Czech Rep.), (1994), 19-30.##7. J. Chvalina, J. Moucka, Hypergroups Determined by Orderings with Regular Endomorphism Monoids, Ital. J. Pure Appl. Math., 16, (2004), 227-242.##8. B. Davvaz, Some Results on Congruences in Semihypergroups, Bull. Malays. Math. Sci. Soc., 23(2), (2000), 53-58.##9. B. Davvaz, Polygroup Theory and Related Systems, World Sci. Publ., Co. Pte. Ltd., Hackensack, NJ, 2013.##10. B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, Palm Harbor, USA, 2007.##11. D. Heidari, B. Davvaz, On Ordered Hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 73(2), (2011), 85-96.##S. Hoskova, Representation of Quasi-Order Hypergroups, Glob. J. Pure Appl. Math., 1, (2005), 173-176.##13. S. Hoskova, Upper Order Hypergroups as a Reflective Subcategory of Subquasiorder Hypergroups, Ital. J. Pure Appl. Math., 20, (2006), 215-222.##14. A. Iampan, Characterizing Ordered Bi-Ideals in Ordered Γ-Semigroups, Iranian Journal of Mathematical Sciences and Informatics, 4(1), (2009), 17-25.##15. D. G. Johnson, A Structure Theory for a Class of Lattice-Ordered Rings, Acta Math., 104, (1960), 163-215.##16. N. Kehayopulu, M. Tsingelis, Pseudoorder in Ordered Semigroups, Semigroup Forum,50, (1995), 389-392.##17. Y. Kemprasit, Multiplicative Interval Semigroups on R Admitting Hyperring Structure,Ital. J. Pure Appl. Math., 11, (2002), 205-212.##18. M. Krasner, A Class of Hyperrings and Hyperfields, Internat. J. Math. and Math. Sci., 6(2), (1983), 307-312.##19. F. Marty, Sur Une Generalization de la Notion de Groupe, 8iem congress Math. Scandinaves, Stockholm, (1934), 45-49. ##20. J. Mittas, Hypergroups Canoniques, Math. Balkanica, 2, (1972), 165-179.##21. W. Phanthawimol, Y. Punkla, K. Kwakpatoon and Y. Kemprasit, On Homomorphisms of Krasner Hyperrings, Analele Stiintifice ale Universitatii, AL.I. CUZA, Mathematica, Tomul LVII, (2011), 239-246.##22. T. Vougiouklis, The Fundamental Relation in Hyperrings, The General Hyperfields, in: Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), World Scientific, 1991, 203-211. ##23. T. Vougiouklis, Hyperstructures and Their Representations, 115, Hadronic Press Inc., Florida, 1994. ## ##]
A Numerical Method For Solving Ricatti Differential Equations
2
2
By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.
51
71
M.
Masjed-Jamei
M.
Masjed-Jamei
K. N. Toosi University of Technology
Iran
mmjamei@kntu.ac.ir
A. H.
Salehi Shayegan
A. H.
Salehi Shayegan
K. N. Toosi University of Technology
Iran
ah.salehi@mail.kntu.ac.ir
Riccati differential equations
Adams-Bashforth rules
Weighting factor
Nonlinear differential equations
Stirling numbers.
[1.S. Abbasbandy, A New Application of He’s Variational Iteration Method for Quadratic Riccati Differential Equation by Using Adomians Polynomials, Journal of Computational and Applied Mathematics, 207, (2007), 59-63.##2. S. Abbasbandy, Iterated He’s Homotopy Perturbation Method for Quadratic Riccati Differential Equation, Applied Mathematics and Computation, 175 , (2006), 581-589.##3. S. Abbasbandy, Homotopy Perturbation Method for Quadratic Riccati Differential Equationan and Comparison with Adomians Decomposition Method, Applied Mathematics and Computation, 172 , (2006), 485-490.##4. H. Aminikhah, M.Hemmatnezhad, An Efficient Method for Quadratic Riccati Differential Equation, Communications in Nonlinear Science and Numerical Simulation, 15, (2010), 835-839.##5. K. Atkinson, W. Ham, D. Stewart, Numerical Solution of Ordinary Differential Equations , Wiley, 2009.##6. H. Bulut, D.J.Evans, On the Solution of the Riccati Equation by the Decomposition Method, International Journal of Computer Mathematics, 79, (2002), 103-109.##7. J. C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, Ltd, 2008.##8. P. L. Butzer, M. Hauss, On Stirling Functions of the Second Kind, Studies in Applied Mathematics, 84, (1991), 71-91.##9. G. Dahlquist, Convergence and Stability in the Numerical Integration of Ordinary Differential Equations, Mathematica Scandinavica, 4, (1956), 33-53.##10. F. Geng , A Modified Variational Iteration Method for Solving Riccati Differential Equations, Computers & Mathematics with Applications, 60, (2010), 1868-1872.##11. F. Geng, Y. Lin, M. Cui, A Piecewise Variational Iteration Method for Riccati Differential Equations, Computers & Mathematics with Applications, 58 , (2009), 2518-2522.##12. M. Gulsu, M. Sezer, On the Solution of the Riccati Equation by the Taylor Matrix Method, Applied Mathematics and Computation, 176, (2006), 414-421.##13. B. Jazbi, M. Moini, Application of Hes Homotopy Perturbation Method for Schr ̈o Dinger Equation, Iranian Journal of Mathematical Sciences and Informatics, 3 (2), (2008), 13-19.##14. M. Lakestani, M. Dehghan, Numerical Solution of Riccati Equation Using the Cubic B-spline Scaling Functions and Chebyshev Cardinal Functions, Computer Physics Communications, 181, (2010), 957-966.##15. M. Masjed-Jamei, On Constructing New Interpolation Formulas Using Linear Operators and an Operator Type of Quadratur Rules, Journal of Computational and Applied Mathematics, 216, (2008), 307-318.##16. M. Masjed-Jamei, On Constructing New Expansions of Functions Using Linear Operators, Journal of Computational and Applied Mathematics, 234, (2010), 365-374.##17. F. Mohammadi, M. M. Hosseini, A Comparative Study of Numerical Methods for Solving Quadratic Riccati Differential Equations, Journal of the Franklin Institute, 348, (2011), 156-164.##18. P. Mokhtary, S. M. Hosseini, Some Implementation Aspects of the General Linear Methods Withinherent Runge-Kutta Stability, Iranian Journal of Mathematical Sciences and Informatics, 3 (1), (2008), 63-76.##19. B. Tang, X. Li, A New Method for Determining the Solution of Riccati Dierential Equations, Applied Mathematics and Computation, 194 , (2007), 431-440.##20. P. Tsai, C. Chen, An Approximate Analytic Solution of the Nonlinear Riccati Differential equation, Journal of the Franklin Institute, 347, (2010), 1850-1862.## ##]
Common Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms
2
2
In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monotone operators.
73
99
M.
Alimohammady
M.
Alimohammady
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran, 47416-1468.
Iran
amohsen@umz.ac.ir
M.
Ramazannejad
M.
Ramazannejad
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran, 47416-1468.
Iran
m.ramzannezhad@gmail.com
Z.
Bagheri
Z.
Bagheri
Azadshahr Branch, Islamic Azad University
Iran
R. J.
Shahkoohi
R. J.
Shahkoohi
Aliabad Katoul Branch Islamic Azad University,
Iran
Maximal monotone operator
Equilibrium problem
Variational inequality.
[1. Y. I. Alber, Metric and Generalized Projection Operators in Banach Space, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (A. G. Kartsatos, ed.), Lecture Notes in Pure and Appl. Math., 178, Dekker, New York,(1996), 15-50.##2. D. Butnariu, S. Reich, Aj. Zaslavski, Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces, J. Appl. Anal., 7, (2001), 151-174.##3. G. Cai, Sh. Bu, Weak Convergence Theorems for General Equlibrium Problems and Variational Inequlity Problems and Fixed Point Problems in Banach Spaces, Acta Math-ematica Scientia, 33B (1), (2013), 303-320.##4. Y. Censor, S. Reich, Iterations of Paracontractions and Firmly Nonexpansive Operators with Applications to Feasibility and Optimization, Optimization, 37, (1996), 323-339.##5. S. Chandok, T. D. Narang, Common Fixed Points and Invariant Approximations for C_q -Commuting Generalized Nonexpansive appings, Iranian Journal of Mathematical Sciences and Informatics, 7(1), (2012), 21-34.##6. Y. J. Cho, H. Zhou, G. Guo, Weak and Strong Convergence Theorems for Three-step Iterations with Errors for Asymptotically Nonexpansive Mappings, Comput Math Appl, 47, (2004), 707-717.##7. I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer, Dordrecht, 1990.##8. M. Eslamian, A, Abkar, Generalized Contractive Multivalued Mappings and Common Fixed Points, Iranian Journal of Mathematical Sciences and Informatics, 8 (2), (2013), 75-84.##9. S. Kamimura, W. Takahashi, Strong Convergence of a Proximal-type Algorithm in a Banach Space, SIAM J. Optim., 13 (3), (2002), 938-945.##10. F. Kohsaka, W. Takahashi, Strong Convergence of an Iterative Sequence for Maximal Monotone Operators in a Banach Space, Abstract and Applied Analysis, 13 (3), (2004), 239-249.##11. S. Martinet, R ́egularisation d in ́equations Variationelles Par Approximations Succesives, Rev. Fr. Inf. Rech. Op ́er., 2 , (1970), 54-159.##12. S. Plubtieng, K. Ungchittrakool, Approximation of Common Fixed Points for a Countable Family of Relatively Nonexpansive Mappings in a Banach Space and Applications, Nonlinear Anal, 72, (2010), 2896-2908.##13. X. Qin, YJ. Cho, SM. Kang, Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems in Banach Spaces, J. Comput. Appl. Math., 225, (2009), 20-30.##14. S. Reich, A Weak Convergence Theorem for the Alternating Method with Bregman Distances, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (A. G. Kartsatos, ed.), Lecture Notes in Pure and Appl. Math., 178 , (1996), 313-318.##15. R. T. Rockafellar, Monotone Operators and the Proximal Point Algorithm, SIAM J. Control Optim., 14, (1976), 877-898. ##16. S. Saewan, Poom Kumam, Y. J. Cho, Convergence Theorems for Finding Zero Points of Maximal Monotone Operators and Equilibrium Problems in Banach, Journal of Inequalities and Applications, (2013).##17. S. M. Soltuz, Observations on Some Sequences Supplied by nequalities, Mathematical Communications, 6 , (2001), 101-106.##18. W. Takahashi, Nonlinear Functional Analysis, Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, , 2000.##19. K. Wattanawitoon, P. Kumam, Modified Proximal Point Algorithm for Finding a Zero Point of Maximal Monotone Operators, Generalized Mixed Equilibrium Problems and Variational Inequalities, Mathematical Communications, 6 , (2001), 101-106.##20. H. K. Xu, Inequalities in Banach Spaces with Applications, Nonlinear Anal, 16 , (1991), 1127-1138.##21. S. Zhang, Generalized Mixed Equlibrium Problem in Banach Spaces, Appl Math Mech Engl Ed., 30, (2009), 11051112. doi:10.1007/s10483-009-0904-6.##22. H. Zegeye, E. U. Ofoedu, N. Shahzad, Convergence Theorems for Equilibrium Problem, Variotional Inequality Problem and Countably Infinite Relatively Quasi-nonexpansive Mappings, Appl Math Comput., 216 , (2010), 3439-3449.##23. H. Zhou, G. Gao, B. Tan, Convergence Theorems of a Modified Hybrid Algorithm for a Family of Quasi--Asymptotically Nonexpansive Mappings, J. Appl. Math. Comput., 32, (2010), 453-464.## ##]
On the $s^{th}$ Derivative of a Polynomial-II
2
2
The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.
101
109
A.
Mir
A.
Mir
University of Kashmir
India
mabdullah_mir@yahoo.co.in
Q.M.
Dawood
Q.M.
Dawood
University of Kashmir
India
B.
Dar
B.
Dar
University of Kashmir
India
darbilal85@ymail.com
Polynomial
Zeros
$s^{th}$ derivative
[1. V. V. Arestov, On Integral Inequalities for Trigonometric Polynomials and Their Derivatives, Izv. Akad. Nauk. SSSR. Ser. Mat., 45, (1981), 3-22.##2. A. Aziz, Q. M. Dawood, Inequalities for a Polynomial and its Derivative, J.Approx. Theory, 54, (1988), 306-313.##3. A. Aziz, N. A. Rather, Some Zygmund Type L_p Inequalities for Polynomials, J.Math. Anal. Appl., 289 , (2004), 14-29.##4. A. Aziz, W. M. Shah, L_p Inequalities for Polynomials with Restricted Zeros, Glas. Mate., 32, (1997), 247-258.##5. A. Aziz, W. M. Shah, L_p Inequalities for Polynomials with Restricted Zeros, Proc. Indian Acad. Sci. (Math. Sci.), 108, (1998), 63-68.##6. S. Bernstein, Lecons Sur Les Proprietes Extremals et la Meilleure Approximation des Fonctions Analytiques d’une Fonctions Reelle , Gauthier-villars Paris, 1926.##7. N. G. De-Bruijn, Inequalities Concerning Polynomials in the Complex Domain, Nederl. Akad. Wetnesch Proc., 50, (1947), 1265-127.##8. M. R. Eslahchi, Sonaz Amani, The Best Uniform Polynomial Approximation of Two Classes of Rational Functions, Iranian Journal of mathematical Sciences and Informatics, 7, (2012), 93-102.##9. N. K. Govil, , Q. I. Rahman, Functions of Exponential Type not Vanishing in a Half-Plane and Related Polynomials, Trans. Amer. Math. oc ., 137, (1969), 501-517. ##10. N. K. Govil, Q. I. Rahman, G. Schemeisser, On the Derivative of a Polynomial, Illinois J. Math., 23, (1979), 319-330.##11. P. D. Lax, Proof of a Conjecture of P. Erd ̈os on the Derivative of a Polynomial, Bull. Amer. Math. Soc., 50, (1944), 509-513.##12. M. A. Malik, On the Derivative of a Polynomial, J. London Math. Soc., 1, (1969), 57-60.##13. Q. I. Rahman, G. Schemeisser, L_p Inequalities for Polynomials, J. Approx. Theory, 53, (1988), 26-32.##14. Rasoul Aghalary, Applications of the Norm Estimates for Univalance of Analytic Functions, Iranian Journal of Mathematical Sciences and Informatics, 9 , (2014), 101-108.##15. A. Zygmund, A Remark on Conjugate Series, Proc. London Math. Soc., 34 , (1932), 392-400.## ##]
Sufficient Inequalities for Univalent Functions
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2
In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.
111
116
R.
Kargar
R.
Kargar
Urmia Branch, Islamic Aza d University
Iran
rkargar1983@gmail.com
A.
Ebadian
A.
Ebadian
Payame Noor University, Tehran.
Iran
ebadian.ali@gmail.com
J.
Sokol
J.
Sokol
University of Rzesz ́o
Poland
jsokol@prz.edu.pl
Analytic
Univalent
Starlike functions
Convex functions
[1. R. Aghalary, Application of the Norm Estimates for Univalence of Analytic Functions, Iranian Journal of Mathematical Sciences and informatics, 9 (2), (2014), 101-108.##2. A.W. Goodman, Univalent Functions, Vols. 1 and 2, Mariner, Tampa, FL, 1983.##3. R. Kargar, A. Ebadian, J. Sok ́o l, Certain Coefficient Inequalities for p-valent Functions, Malaya J. Mat., 4 (1), (2016), 37-41.##4. M. Nunokawa, N.E. Cho, O.S. Kwon, J. Sok ́o l, On Differential Subordinations in the Complex Plane, Journal of Inequalities and applications, 2015 (1), (2015), 7.##5. M. Nunokawa, S. Owa, K. Kuroki, J. Sok ́o l, Some Generalizition Properties of Analytic Functions Concerned with Sakaguchi Result, Tamkang Journal of Mathematics, 46 (2), (2015), 143-150.##6. M. Obradovi ́c, S. Ponuusamy, N. Tuneski, Radius of Univalence of Certain Combination of Univalent of Analytic functions, Bull. Malays. math. Sci. Soc., 35 (2), (2012), 325-334.##7. A. Taghavi, R. Hosseinzadeh, Uniform Boundedness Principle for Operators on Hyper- vector spaces, Iranian Journal of Mathematical Sciences and Informatics, 7 (2), (2012), 9-16. ## ##]
Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones
2
2
In this paper, we define the almost uniform convergence and
the almost everywhere convergence for cone-valued functions with respect
to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R
is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone
and (Q, W) is a locally convex complete lattice cone.
117
125
D.
Ayaseh
D.
Ayaseh
University of Tabriz
Iran
d_ayaseh@tabrizu.ac.ir
A.
Ranjbari
A.
Ranjbari
University of Tabriz
Iran
ranjbari@tabrizu.ac.ir
Locally convex cones
Egoroff Theorem
Operator valued measure.
[1. D. Ayaseh, A. Ranjbari, Bornological Convergence in Locall Convex Cones, Mediterr. J. Math., 13 (4), (2016), 1921-1931.##2. D. Ayaseh, A. Ranjbari, Bornological Locally Convex Cones, Le Matematiche, 69 (2), (2014), 267-284.##3. D. Ayaseh, A. Ranjbari, Locally Convex Quotient Lattice Cones, Math. Nachr., 287 (10), (2014), 1083-1092.##4. D. Ayaseh, A. Ranjbari, Some Notes on Bornological and Nonbornological Locally Convex Cones, Le Matematiche, 70 (2), (2015), 35-241.##5. N. Eftekhari, The Basic Theorem and it’s Consequences, Iranian Journal of Mathematical Sciences and Informatics, 4 (1), (2009), 27-35.##6. P. R. Halmos, Measure Theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504.##7. K. Keimel, W. Roth, Ordered Cones and Approximation, Lecture Notes in Mathematics, 1517, 1992, Springer Verlag, Heidelberg-Berlin-new York.##8. A. Ranjbari, Strict Inductive Limits in Locally Convex Cones, Positivity, 15 (3), (2011), 465–471. ##9. W. Roth, Operator-valued Measures and Integrals for Cone-valued Functions, Lecture Notes in Mathematics, 1964, 2009, Springer erlag, Heidelberg-Berlin-New York. ##10. A. Taghavi, R. Hosseinzadeh, Uniform Boundedness Principle for Operators on Hyper-vector Spaces, Iranian Journal of Mathematical Sciences and Informatics, 7 (2), (2012), 9-16. ## ##]
Order Almost Dunford-Pettis Operators on Banach Lattices
2
2
By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F that is order almost Dunford-Pettis and weak almost Dunford-Pettis is an almost weakly lim- ited operator.
127
139
H.
Ardakani
H.
Ardakani
Yazd University
Iran
halimeh_ardakani@yahoo.com
S. M. S.
Modarres Mosadegh
S. M. S.
Modarres Mosadegh
Yazd University
Iran
smodarres@yazd.ac.ir
Order Dunford-Pettis operator
Weakly limited operator
Almost Dunford-Pettis set.
[1. C. D. Aliprantis, O. Burkishaw, Positive operators, Academic Press, New York and London, 1978.##2. K. T. Andrews, Dunford-Pettis Sets in the Space of Bochner Integrable Functions, Math. Ann., 241, (1979), 35-41.##3. B. Aqzzouz, K. Bouras, Dunford-Pettis Sets in Banach Lattices, Acta Math. Univ. Comenianae, 2, (2012), 185-196.##4. H. Ardakani, S. M. S. Modarres Mosadegh, Strong Relatively Compact Dunford-Pettis Property in Banach Lattices, accepted in Annals of functional Analysis. ##5. K. Bouras, M. Moussa, Banach lattices with weak Dunford-Pettis property, Int. J. of Info. and Math. Sciences, 6, (2010), 203-207.##6. J. Bourgain, J. Diestel, Limited Operators and Strict Cosingularity, Math. Nachr., 119, (1984), 55-58.##7. K. Bouras, E. Kaddouri, J. Hmichane, M. Moussa, The class of ordered Dunford-Pettis operators, Mathematica Bohemica, 138, (2013), 89(297). ##8. K. Bouras, Almost Dunford-Pettis Sets in Banach Lattices, Rend. Circ. Mat. Palermo, 62, (2013), 227-236.##9. J. X. Chen, Z. L. Chen, G. X. Ji, Almost Limited Sets in Banach Lattices, J. Math. Anal. Appl., 412, (2014), 547-563.##10. P. G. Dodds, D. H. Fremlin, Compact Operators on Banach Lattices, Israel J. Math., 34, (1979), 287-320.##11. A. Elbour, N. Machrafi, M. Moussa, On the class of weak and almost limited operators, arXiv:1403.0136v1.##12. A. E. Kaddouri, M. Moussa, About the Class of Ordered Limited Operators, Acta Universitatis Carolinae. Mathematica et Physica, 54, (2013), 37-43.##13. A. E. Kaddouri, K. EL. Fahri, J. Hmichane, M. Moussa, The class of ordered almost limited operators on Banach lattices, submitted to acta Math. Univ. Comenianae. ##14. H. Z. Lin, The Weakness of Limited Set and Limited Operator in Banach Spaces, Pure Appl. Math., 27, (2011), 650-655.##15. P. Meyer- Nieberg, Banach lattices, Universitext, springer- Verlag, Berlin, 1991.##16. N. Machrafi, A. Elbour, M. Moussa, Some Characterizations of Almost Limited Sets and Applications, arXiv:1312.2770v1.##17. J. A. Sanchez, Operators on Banach Lattices (Spanish), Ph. D. Thesis, Complutense University, Madrid, 1985.##18. J. A. Sanchez, Positive Schur Property in Banach Lattices, Extraccta Math., 7, (1992), 161-163.##19. W. Wnuk, Banach Lattices with the weak Dunford{Pettis Property, Atti Sem. Mat. Univ. Modena XLII, (1994), 227-236.## ##]
Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
2
2
Let $R$ be a prime ring with its Utumi ring of quotients $U$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate}
item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=mp x$ for all $x in R$; item char $(R)=2$ and $R$ satisfies $s_4$;item char $(R) neq 2$, $R$ satisfies $s_4$ and there exists $bin U$ such that $F(x)=bx$ for all $x in R$.
141
153
B.
Dhara
B.
Dhara
Belda College
India
basu_dhara@yahoo.com
K.G.
Pradhan
K.G.
Pradhan
Belda College
India
kgp.math@gmail.com
Sh.K.
Tiwari
Sh.K.
Tiwari
IIT- Delhi
India
shaileshiitd84@gmail.com
Prime ring
Generalized derivation
Utumi quotient ring.
[1. A. Ali, N. ur Rehman, S. Ali, On Lie Ideals with Derivations as Homomorphisms and Anti-Homomorphisms, Acta Math. Hung., 101 (1–2), (2003), 79–82.##2. K. I. Beidar, W. S. Martindale III, A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Math., 196, (1996). New York: Marcel Dekker, Inc. ##3. H. E. Bell, L. C. Kappe, Rings in Which Derivations Satisfy Certain Algebraic Conditions, Acta Math. Hung., 53, (1989), 339–346. ##4. J. Bergen, I. N. Herstein, J. W. Kerr, Lie Ideals and Derivations of Prime Rings, J. Algebra, 71, (1981), 259–267.##5. M. Bresar, On the Distance of the Composition of Two Derivations to be the Generalized Derivations, Glasgow Math. J., 33, (1991), 89–93.##6. C. L. Chuang, GPIs Having Coefficients in Utumi Quotient Rings, Proc. Amer. Math. Soc., 103, (1988), 723–728.##7. C. L. Chuang, The Additive Subgroup Generated by a Polynomial, Israel J. Math., 59 (1), (1987), 98–106.##8. V. De Filippis, N. ur Rehman, A. Z. Ansari, Lie Ideals and Generalized Derivations in Semiprime Rings, Iranian Journal of Mathematical Sciences and Informatics, 10 (2), (2015), 45–54. ##9. V. De Filippis, Generalized Derivations as Jordan Homomorphisms on Lie Ideals and Right Ideals, Acta Math. Sinica, English Series, 25 (2), (2009), 1965–1974.##10. B. Dhara, N. Argac, K. G. Pradhan, Annihilator Condition of a Pair of Derivations in Prime and Semiprime Rings, Indian J. Pure Appl. math., 47 (1), (2016), 111–124.##11. B. Dhara, S. Kar, K. G. Pradhan, Generalized Derivations Acting as Homomorphisms or anti-Homomorphisms with Central Values in Semiprime Rings, Miskolc Math. Notes, 16 (2), (2015), 781–791.##12. B. Dhara, Sh. Sahebi, V. Rahmani, Generalized Derivations as a Generalization of Jordan Homomorphisms on Lie Ideals and Right Ideals, Math. Slovaca, 65 (5), (2015), 963–974.##13. B. Dhara, Sh. Sahebi, V. Rahmani, Generalized Derivations as a Generalization of Jordan Homomorphisms Acting on Lie Ideals, Matematiki Vesnik, 67 (2), (2015), 92–101.##14. B. Dhara, S. Kar, D. Das, A Multiplicative (generalized)-(σ, σ)-Derivation Acting as (anti-)Homomorphism in Semiprime Rings, Palestine J. Mathematics, 3 (2), (2014), 240–246.##15. B. Dhara, Generalized Derivations Acting as Homomorphism or anti-Homomorphism in Semiprime Rings, Beitr. Algebra Geom., 53, (2012), 203–209.##16. A. Ebadian, M. E. Gordji, Left Jordan Derivations on Banach Algebras, Iranian Journal of Mathematical Science and Informatics, 6 (1), (2011), 1–6.##17. T. S. Erickson, W. S. Martindale III, J. M. Osborn, Prime Non associative Algebras, Pacific J. Math., 60, (1975), 49–63. ##18. O. Golbasi, K. Kaya, On Lie Ideals with Generalized Derivations, Siberian Math. J., 47 (5), (2006), 862–866. ##19. I. Gusic, A Note on Generalized Derivations of Prime Rings, Glasnik Mate., 40 (60), (2005), 47–49.##20. N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37.Providence, RI: Amer. Math. Soc., 1964.##21. V. K. Kharchenko, Differential Identity of Prime Rings, Algebra and Logic, 17, (1978), 155–168. ##22. C. Lanski, S. Montgomery, Lie Structure of Prime Rings of Characteristic 2, Pacific J. Math., 42 (1), (1972), 117–136.##23. T. K. Lee, Generalized Derivations of Left Faithful Rings, Comm. Algebra, 27 (8), (1999), 4057–4073.##24. T. K. Lee, Semiprime Rings with Differential Identities, Bull. Inst. Math. Acad. Sinica, 20 (1), (1992), 27–38. ##25. W. S. Martindale III, Prime Rings Satistying a Generalized Polynomial Identity, J. Algebra, 12, (1969), 576–584.##26. N. ur Rehman, M. A. Raza, Generalized Derivations as Homomorphisms or anti-Homomorphisms on Lie Ideals, Arab J. Math. Sc., 22 (1), (2016), 22–28.##27. Y. Wang, H. You, Derivations as Homomorphisms or anti-Homomorphisms on Lie Ideals, Acta Math. Sinica, English Series, 23 (6), (2007), 1149–1152.## ##]
ABSTRACTS IN PERSIAN Vol.12, No.2
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2
Please see the full text contains the Pesian abstracts for this volume.
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165
Name of Authors In This Volume
Name of Authors In This Volume
IJMSI, Tarbiat Modares University
Iran
ABSTRACTS
PERSIAN
Vol. 12
No. 2
[All references of vol12no2## ##]