1 1735-4463 ACECR at Tarbiat Modares University 802 Special Multipliers of pg-Bessel sequences in Banach spaces Abdollahpour M. R. Najati A. c Gavruta P. d c Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili d Department of Mathematics, Politehnica University of TimiΒΈsoara, PiatΒΈa Victoriei 1 10 2020 15 2 1 12 17 11 2015 22 05 2020 In this paper, we introduce $(p,q)g-$Bessel multipliers in Banach spaces and we show that under some conditions a $(p,q)g-$Bessel multiplier is invertible. Also, we show the continuous dependency of $(p,q)g-$Bessel multipliers on their parameters.
859 General Characteristics of Common Neighborhood Graph under Graph Operations and on Cayley Graphs Sedghi Sh. e Lee D.-W. f Shobe N. g e Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran f Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea. g Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran 1 10 2020 15 2 13 20 07 03 2016 27 03 2020 Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its congraphs. 1088 General On the Hyponormal Property of Operators Nabavi Sales S. M. S. h h Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran 1 10 2020 15 2 21 30 22 05 2017 04 05 2020 Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge transform, $tilde{T}_{f}$. Given two continuous functions $f$ and $g$ with the property  $f(t)g(t)=t$, we also introduce the $(f,g)$-Aluthge transform, $tilde{T}_{(f,g)}$. The features of these transforms are discussed as well. 1131 General Approximate Solution of Linear Volterra-Fredholm Integral Equations and Systems of Volterra-Fredholm Integral Equations Using Taylor Expansion Method Didgar M. i Vahidi A.R. j i Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran. j Department of Mathematics, College of Science, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University , Tehran, Iran. 1 10 2020 15 2 31 50 13 08 2017 13 02 2018 In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equations with respect to unknown function and its derivatives. An approximate solution can be easily determined by solving the obtained system. Furthermore, this method leads always to the exact solution if the exact solution is a polynomial function of degree up to n. Also, an error analysis is given. In addition, some problems are provided to demonstrate the validity and applicability of the proposed method. 1133 Special On Subclasses of Analytic and m-Fold Symmetric Bi-Univalent Functions K. Wanas A k H. Majeed A. l k Department of Mathematics, College of Science, Baghdad University l Department of Mathematics, College of Science, Baghdad University 1 10 2020 15 2 51 60 17 08 2017 26 06 2018 The purpose of the present paper is to introduce and investigate two new subclasses π’¦π›΄π‘š(πœ†,𝛾;𝛼) and 𝒦∗π›΄π‘š(πœ†,𝛾;𝛽) of π›΄π‘š consisting of analytic and π‘š-fold symmetric bi-univalent functions defined in the open unit disk π‘ˆ. We obtain upper bounds for the coefficients |π‘Žπ‘š+1| and |π‘Žπ‘š| for functions belonging to these subclasses. Many of the well-known and new results are shown to follow as special cases of our results. 1135 General Lommel Matrix Functions Shehata A. m m Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt 1 10 2020 15 2 61 76 21 08 2017 15 01 2018 The main objective of this work is to develop a pair of Lommel matrix functions suggested by the hypergeometric matrix functions and some of their properties are studied. Some properties of the hypergeometric and Bessel matrix functions are obtained. 1144 General Uniform Number of a Graph Kumar A. n Mohankumar E. o n Amrita Vishwa Vidyapeetham, Amrita University, India. o Amrita Vishwa Vidyapeetham, Amrita University, India. 1 10 2020 15 2 77 99 03 09 2017 06 07 2019 We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ is power set of $X = {D(x_i, x_j): x_i neq x_j}.$ We obtain some basic results and compute the newly introduced graph parameter for some specific graphs. 1140 Special Roman k-Tuple Domination in Graphs P. Kazemi A. p p U. of Mohaghegh Ardabili 1 10 2020 15 2 101 115 29 08 2017 08 01 2020 For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$‎, ‎we define a‎ ‎function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating‎ ‎function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least‎ ‎$k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$‎. ‎The minimum weight of a Roman $k$-tuple dominating function $f$ on $G$ is called the Roman $k$-tuple domination number of the graph where the weight of $f$ is $f(V)=sum_{vin V}f(v)$‎. ‎In this paper‎, ‎we initiate to study the Roman $k$-tuple‎ ‎domination number of a graph‎, ‎by giving some sharp bounds for the Roman $k$-tuple domination number of a garph‎, ‎the Mycieleskian of a graph‎, ‎and the corona graphs‎. ‎Also finding the Roman $k$-tuple domination number of some known graphs is our other goal‎. ‎Some of our results extend these one‎ ‎given by Cockayne and et al‎. ‎cite{CDHH04} in 2004 for the Roman‎ ‎domination number‎. 1145 General A Note on Belief Structures and S-approximation Spaces Shakiba A. Kafshdar Goharshady A. Hooshmandasl M. R. Alambardar Meybodi M. Vali-e-Asr University of Rafsanjan Institute of Science and Technology Austria (IST Austria) University of Mohaghegh Ardabili University of Isfahan 1 10 2020 15 2 117 128 04 09 2017 29 03 2020 We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempster's multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space.  1146 Special Stability and Bifurcation of an SIS Epidemic Model with Saturated Incidence Rate and Treatment Function kamel Naji R. Adnan Thirthar A. Department of Mathematics, College of Science,University of Baghdad, Baghdad, Iraq Department of Mathematics, College of Science,University of Baghdad, Baghdad, Iraq 1 10 2020 15 2 129 146 06 09 2017 21 03 2018        In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these equilibrium points are established using Lyapunov method. The local bifurcation near the disease free equilibrium point is investigated. Hopf bifurcation condi- tion, which may occurs around the endemic equilibrium point is obtained. The conditions of backward bifurcation and forward bifurcation near the disease free equilibrium point are also determined. Finally,numerical simulations are given to investigate the global dynamics of the system and con rm the obtained analytical results. 1150 General Existence and Iterative Approximations of Solution for Generalized Yosida Approximation Operator Akram M. Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 107, KSA 1 10 2020 15 2 147 161 12 09 2017 14 02 2018 In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and generalized Yosida approximation operator. We also furnish an illustrative example to demonstrate our results. Furthermore, we suggest an iterative algorithm to solve a Yosida inclusion problem under some mild conditions in q-uniformly smooth Banach space and discuss the convergence and uniqueness of the solution.  1154 General The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials Ghaderi N. Farahi M. H. ferdowsi university of mashhad ferdowsi university of mashhad 1 10 2020 15 2 163 181 17 09 2017 01 05 2018 ‎In this paper‎, ‎we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays‎. ‎Constant or pantograph delays may appear in state-control or both‎. ‎We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then‎, ‎these are utilized to reduce the solution of optimal control with constant and pantograph delay to the solution of nonlinear programming‎. ‎In truth‎, ‎the principal problem can be transferred to the quadratic programming problem‎. ‎Some examples are included to demonstrate the validity and applicability of the technique. 1179 Special Sharply $(n-2)$-transitive Sets of Permutations N. Iradmusa M. Shahid Beheshti University 1 10 2020 15 2 183 190 12 10 2017 03 12 2018 Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called emph{sharply $t$-transitive} if for any given pair of $t$-tuples, exactly one element of $S$ carries the first to the second. In addition, a subset $S$ of $S_n$ is called $t$-intersecting if $fix(h^{-1}g)geq t$ for any two distinct permutations $h$ and $g$ of $S$. In this paper, we prove that there are only two sharply $(n-2)$-transitive subsets of $S_n$ and finally we establish some relations between sharply $k$-transitive subsets and $t$-intersecting subsets of $S_n$ where $k,tin mathbb{Z}$ and $0leq tleq kleq n$. 1181 General Some Properties of Vector-valued Lipschitz Algebras Azizi M. Biyabani E. Rejali A. Department of Mathematics, University of Isfahan, Isfahan, Iran. Department of Mathematics, University of Isfahan, Isfahan, Iran. Department of Mathematics, Islamic Azad University, majlesi Branch, Isfahan, Iran 1 10 2020 15 2 191 205 15 10 2017 18 12 2018 ‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$. 2014 Special ABSTRACTS IN PERSIAN Vol.15, No.2 in this Volume The Name of Authors Tarbiat Modares University (TMU) 1 10 2020 15 2 207 221 15 11 2020 15 11 2020 Please see the full text contains the Pesian abstracts for this volume.