Fixed Point Theorems for Multi-valued Nonexpansive Mappings in Banach Spaces
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In this paper, we present new fixed point theorems for multivalued nonexpansive mappings. Since Banach space can have any geometric structure, we consider mappings such that their perturbation by the identity operator is expansive. Then we derive some fixed point results including existence theorems for the sum and product of some classes of nonlinear operators. Three illustrating examples for functional and differential inclusions are supplied.
KeywordsMultivalued nonexpansive map \(\psi \)-expansive map sum of operators product of operators banach algebra
Mathematics Subject Classification47H09 47H10 47J25
The authors would like to thank the anonymous referee for his/her careful reading of the original manuscript which led to substantial improvement of the paper.
- 1.Aubin, J., Cellina, A.: Differential inclusions. Set-valued Maps and Viability Theory. Grundlehren der Mathematischen Wissenschaften, vol. 264. Springer, Berlin (1984)Google Scholar
- 5.Deimling, K.: Multivalued Differential Equations, Walter de Gruyter Series in Nonlinear Analysis and Applications, vol. 1. Walter de Gruyter Co., Berlin (1992)Google Scholar
- 8.Djebali, S.: Fixed point theory for \(1\)-set contractions: a survey, applied mathematics in Tunisia. In: Proceedings of the International Conference on Advances in Applied Mathematics (ICAAM), Hammamet, Tunisia, December 2013. Series. Springer Proceedings in Mathematics & Statistics, vol. 131, pp. 53–10. Springer-Birkhäuser (2015)Google Scholar
- 13.Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83. Marcel Dekker, New York (1984)Google Scholar