Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces
Worawut Laowang, Bancha Panyanak · Fixed Point Theory and Applications · 2011
Abstract Abkar and Eslamian (Nonlinear Anal. TMA,74, 1835-1840, 2011) prove that ifKis a nonempty bounded closed convex subset of a complete CAT(0) spaceX,t:K→Kis a single-valued quasi-nonexpansive mapping andT:K→KC(K) is a multivalued mapping satisfying conditions (E) and (Cλ) for someλ∈ (0, 1) such thattandTcommute weakly, then there exists a pointz∈Ksuch thatz=t(z) ∈T(z). In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E) ofTcan be weakened to the strongly demiclosedness ofI-T.