Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions
Tóm tắt
In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on nonempty, closed convex set of Banach algebras are also presented. These results improve and complement a number of earlier works. As an application, we prove existence results for a broad class of nonlinear functional integral inclusions as well as nonlinear differential inclusions.
Tài liệu tham khảo
Agarwal, R.P., Meehan, M., O’Regan, D.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge (2001)
Amara, K.B., Jeribi, A., Kaddachi, N.: New fixed point theorems for countably condensing maps with an application to functional integral inclusions. Mathematica Slovaca. 71, 1487–1510 (2021)
Banaś, J., Olszowy, L.: On the equivalence of some concepts in the theory of Banach algebras. Ann. Funct. Anal. 10, 277–283 (2019)
Ben Amara, K., Jeribi, A., Kaddachi, N.: Equivalence of some properties in the theory of Banach algebras and applications. Journal of Mathematical Analysis and Applications. 520, 126865 (2023)
Ben Amar, A., Boumaiza, M., O’Regan, D.: Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting. J. Fixed Point Theory Appl. 18, 327–350 (2016)
Ben Amar, A., Chouayekh, S., Jeribi, A.: New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations. J. Funct. Anal. 259, 2215–2237 (2010)
Ben Amar, A., Chouayekh, S., Jeribi, A.: Fixed point theory in a new class of Banach algebras and application. Afr. Mat. 24, 705–724 (2013)
Ben Amar, A., Derbel, S., O’Regan, D., Xiang, T.: Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces. J. Fixed Point Theory Appl. 21, 8 (2019). https://doi.org/10.1007/s11784-018-0644-0
Ben Amar, A., O’Regan, D.: Measures of weak noncompactness and fixed point theory in Banach algebras satisfying condition \((\cal{P} )\). Fixed Point Theory 18, 37–46 (2017)
Ben Amar, A., O’Regan, D.: Topological Fixed Point Theory for Single Valued and Multivalued Mappings and Applications. Springer, Cham (2016). (ISBN: 978-3-319-31947-6; 978-3-319-31948-3)
Ben Amar, A., O’Regan, D., Touati, A.: Fixed point theorems for the sum of (ws)-compact and asymptotically \(\Phi \)-nonexpansive mappings. J. Fixed Point Theory Appl. 18, 771–784 (2016)
Browder, F.E.: Nonexpansive nonlinear operators in a Banach space. Proc. Natl. Acad. Sci. USA 54, 1041–1044 (1965)
Cardinali, T., Papalini, F.: Fixed point theorems for multifunctions in topological vector spaces. J. Math. Anal. Appl. 186, 769–777 (1994)
Cichoń, M.: Weak solution of differential equations in Banach spaces. Discuss. Math. Differ. Incl. 15, 5–14 (1995)
De Blasi, F.S.: On a property of the unit sphere in a Banach space. Bull. Math. Soc. Sci. Math. Roumanie 21, 259–262 (1977)
Dhage, B.C.: Multivalued mappings and fixed points II. Tamkang J. Math. 37, 27–46 (2006)
Dhage, B.C.: Some nonlinear alternatives in Banach algebras with applications I. Kyungpook Math. J. 12, 271–283 (2005)
Dhage, B.C.: Some nonlinear alternatives in Banach algebras with applications II. Kyungpook Math. J. 45, 281–292 (2005)
Diestel, J., Uhl, J.J., Jr.: Vector Measures. Mathematical Surveys, 15. American Mathematical Society, Providence (1977)
Fahem, A., Jeribi, A., Kaddachi, N.: Existence of solutions for an integral equation of Chandrasekhar type in Banach algebras with respect to the weak topology. Operator Theory. 177–182 (2021)
G\(\ddot{o}\)hde, D.: Zum Prinzip der Kontraktiven Abbildung. Math. Nachr. 30, 251–258 (1965)
Husain, T., Latif, A.: Fixed points of multivalued nonexpansive maps. Math. Jpn. 33, 385–391 (1988)
Husain, T., Tarafdar, E.: Fixed point theorems for multi-valued mappings of non-expansive type. Yokohama Math. J. 28, 1–6 (1980)
Kim, In-Sook.: Index formulas for countably \(k\)-set contractive operators. Nonlinear Anal. 69, 4182–4189 (2008)
Ishikawa, S.: Fixed points by a new iteration method. Proc. Am. Math. Soc. 44, 147–150 (1974)
Jeribi, A., Kaddachi, N., Krichen, B.: Fixed-point theorems for multivalued operator matrix under weak topology with an application. Bull. Malays. Math. Sci. Soc. 43, 1047–1067 (2020)
Jeribi, A., Kaddachi, N., Krichen, B.: Existence results for a coupled system of perturbed functional differential inclusions in Banach algebras. Bull. Malays. Math. Sci. Soc. 41, 893–918 (2018)
Jeribi, A., Kaddachi, N., Krichen, B.: Existence results for a system of nonlinear functional integral equations in Banach algebras under weak topology. Fixed Point Theory 18, 247–268 (2017)
Jeribi, A., Kaddachi, N., Laouar, Z.: Fixed point theorems for weakly asymptotically regular mappings in Banach spaces with an application. Numerical Functional Analysis and Optimization. 43(1), 68–87 (2022)
Jeribi, A., Kaddachi, N., Laouar, Z.: Generalized form of fixed-point theorems in generalized Banach algebra relative to the weak topology with an application. Filomat. 36(18), 6253–6268 (2022)
Jeribi, A., Krichen, B.: Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory Under Weak Topology for Nonlinear Operators And Block Operator Matrices With Applications (Monographs and Research Notes in Mathematics). CRC Press/Taylor and Francis, Boca Raton (2015)
Jeribi, A., Krichen, B., Mefteh, B.: Fixed point theory in \(WC\)-Banach algebras. Turk. J. Math. 40, 283–291 (2016)
Jeribi, A., Krichen, B., Mefteh, B.: Existence solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations. J. Biol. Dyn. 7, 218–232 (2013)
Kaddachi, N.: Generalized form of fixed point theorems in Banach algebras under weak topology with an application. Filomat 33(13), 4281–4296 (2019)
Kaddachi, N.: Existence results of ordinary differential inclusions in Banach algebra under weak topology. J. Phys. Math. (2018). https://doi.org/10.4172/2090-0902.1000285
Kirk, W.A.: A fixed point theorem for mappings which do not increase distance. Am. Math. Mon. 72, 1004–1006 (1965)
Mitchell, A.R., Smith, C.K.L., An existence theorem for weak solutions of differential equations in Banach spaces. In: Nonlinear Equations in Abstract Spaces (Proceedings of the International Symposium, University of Texas, Arlington, Texas, 1977), pp. 387–404. Academic Press, New York (1978)
Pettis, B.J.: On integration in vector spaces. Trans. Am. Math. Soc. 44, 277–304 (1938)