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Alsheikh Ali A, Ben Amar A. Fixed Point Theorems for Multivalued Mappings in Banach Algebras and an Application for Fractional Integral Inclusion. IJMSI 2026; 21 (1) :107-131
URL: http://ijmsi.ir/article-1-2186-en.html
URL: http://ijmsi.ir/article-1-2186-en.html
Abstract:
In this paper, we establish some fixed point results for the sum and the product of three multivalued mappings, with weakly sequentially closed graph under weak topology features in a Banach algebra. Satisfying a certain sequential condition (P). As an application, our results are used to prove the existence of solutions for a certain non-linear integral inclusion of fractional order.
Keywords: Measures of weak non-compactness, Multivalued mapping, Weakly condensing, Weakly sequentially closed graph, Fixed point theorems, Integral inclusion.
Type of Study: Research paper |
Subject:
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References
1. A. A. Ali, A. Ben Amar, D. O'Regan, Fixed Point Theorems for the Sum of Two Multivalued Mappings and an Application to an Integral Inclusion, Bull. Malays. Math. Sci. Soc., 40, (2017), 1307-1320. [DOI:10.1007/s40840-015-0110-8]
2. A. A. Ali, A. Ben Amar, Measures of Weak Non Compactness, Nonlinear Leray-Schauder Alternatives in Banach Algebras Satisfying Condition P and an Application, Quaestiones Mathematicae, 39(3), (2016). [DOI:10.2989/16073606.2015.1070378]
3. J. Bana's, M. A. Taoudi, Fixed Points and Solutions of Operators Equations for the Weak Topology in Banach Algebras, Taiwanese Journal of Mathematics, 18(3), (2014), 871-893. [DOI:10.11650/tjm.18.2014.3860]
4. A. Ben Amar, A. Jeribi, R. Moalla, Leray-Schauder Alternatives in Banach Algebra Involving Three Operators with Application, Fixed Point Theory, 15(2), (2014), 359-372.
5. A. Ben Amar, S. Chouayekh, A. Jeribi, New Fixed Point Theorems in Banach Algebras under Weak Topology Features and Applications to Nonlinear Integral Equations, J. Funct. Anal., 259(9), (2010), 2215-2237. [DOI:10.1016/j.jfa.2010.06.016]
6. A. Ben Amar, A. Sikorska-Nowak, On Some Fixed Point Theorems for 1-Set Weakly Contractive Multi-Valued Mappings with Weakly Sequentially Closed Graph, Advances in Pure Mathematics, 1, (2011), 163-169. [DOI:10.4236/apm.2011.14030]
7. A. Ben Amar, S. Chouayekh, A. Jeribi, Fixed Point Theory in a New Class of Banach Algebras and Application, Afr. Mat., (2013), 725-742.
8. A. Ben Amar, D. O'Regan, Measures of Weak Non-compactness and Fixed Point Theory in Banach Algebra Satisfying Condition (P), Fixed Point Theory, 18, (2017), 37-46. [DOI:10.24193/fpt-ro.2017.1.04]
9. A. Ben Amar, Krasnoselskii Type Fixed Point Theorems for Multi-valued Mappings with Weakly Sequentially Closed Graph, Ann. Univ. Ferrara, 58(1), (2012), 1-10. [DOI:10.1007/s11565-011-0146-0]
10. A. Ben Amar, M. Boumaiza, D. O'Regan, Hybrid Fixed Point Theorems for Multi-valued Mappings in Banach Algebras under a Weakly Topology Setting, Fixed Point Theory and Applications, 18(2), (2016), 327-350. [DOI:10.1007/s11784-016-0289-9]
11. Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis, 3nd Edition, Springer-Verlag Berlin Heidelberg, 2006.
12. Corneliu Ursescu, Multifunctions With Convex Closed Graph, Czechoslovak Mathematical Journal, Praha, 25(100), (1975). [DOI:10.21136/CMJ.1975.101337]
13. F. S. De Blasi, On a Property of the Unit Sphere in Banach Space, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 21, (1977), 259-262.
14. B. C. Dhage, S. Ntouyas, Ch. Tsamatos, A Fixed Point Theorem and its Applications to Non-linear Integral Equations in Banach Algebra, Greek Mathematical Society, (2002), 119-127.
15. B. C. Dhage, On Some Non-linear Alternatives of Leray-Schauder Type and Functional Integral Equations, Arch. Math.(Brno), 42(1), (2006), 11-23.
16. B. C. Dhage, Multi-Valued Mappings and Fixed Points II, Tamkang Journal Of Mathematics, 37(1), (2006), 27-46. [DOI:10.5556/j.tkjm.37.2006.177]
17. B. C. Dhage, Multi-Valued Operators and Fixed Point Theorems in Banach Algebra I, Taiwainaise Journal Of Mathematics, 10(4), (2006), 1025-1045. [DOI:10.11650/twjm/1500403891]
18. I. Dobrakov, On Representation Of Linear Operators On C0(T, X), Czechoslovak Mathematical Journal, 21(1), (1971), 13-30. [DOI:10.21136/CMJ.1971.101000]
19. L. Gorniewicz, Topological Fixed Point Theory of Mul-tivalued Mappings, 2nd Edition, Springer, New York, 2006.
20. D. O'Regan, M. A. Taoudi, Fixed Point Theorems for the Sum of Two Weakly Sequentially Continuous Mappings, Non-linear Analysis, 73, (2010), 283-289. [DOI:10.1016/j.na.2010.03.009]
21. H. L. Royden, Real Analysis, 3rd Edition, Macmillan Company, New York, 1988.
22. E. Zeidler, Non-linear Functional Analysis and its Applications, I, Springer, New York, 1986. [DOI:10.1007/978-1-4612-4838-5]
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