The Homotopic Invariance for Fixed Points of Set-valued Mappings in Banach Spaces

Abstract We obtain the homotopic invariance for fixed points of set-valued contractions and nonexpansive mappings whose domain is a bounded nonexpansive retract and nonempty interior subset of a uniformly convex Banach space. This gives a partial answer to a problem posed by Sims

Fixed point theorems for multivalued mappings in modular function spaces

The purpose of this paper is to study the existence of fixed points for multivalued nonexpansive mappings in modular function spaces. We apply our main result to obtain fixed point theorems for multivalued mappings in the Banach spaces L1 and l1.Thailand Research FundDirección General de Enseñanza SuperiorJunta de AndalucíaRoyal Golden Jubilee progra

Fixed Points of Multivalued G-Nonexpansive Mappings in Hadamard Spaces Endowed with Graphs

A fixed-point theorem for multivalued G-nonexpansive mappings in Hadamard spaces is proved. The strong convergence theorems of Browder’s and Halpern’s iterations are also established. Our results generalize and improve the results of Tiammee et al. (2015), Alfuraidan and Khamsi (2015), Anakkamatee and Tongnoi (2019), and many others

Noor iterations for asymptotically nonexpansive mappings in CAT(0) spaces

Abstract In this paper, Δ and strong convergence theorems are established for the Noor iterations of asymptotically nonexpansive mappings in CA

Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces

Abstract Abkar and Eslamian (Nonlinear Anal. TMA, 74, 1835-1840, 2011) prove that if K is a nonempty bounded closed convex subset of a complete CAT(0) space X, t : K &#8594; K is a single-valued quasi-nonexpansive mapping and T : K &#8594; KC(K) is a multivalued mapping satisfying conditions (E) and (C&#955;) for some &#955; &#8712; (0, 1) such that t and T commute weakly, then there exists a point z &#8712; K such that z = t(z) &#8712; T(z). In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E) of T can be weakened to the strongly demiclosedness of I - T.</p