Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

Abstract

In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. 2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L τ spaces; our result generalizes a recent result of Domínguez-Benavides et al. 2009 .

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

“…In this paper, we extend this result to the general setting of uniformly convex metric spaces in the sense of Goebel and Reich [24]. Nevertheless, condition (E) of T can be weakened to the strongly demiclosedness of I -T. Since uniformly convex Banach spaces and CAT(0) spaces are uniformly convex metric spaces, then our results extend and improve the results in [4,25,26,23,27] and many others.…”

Fixed point theory for multivalued generalized nonexpansive mappings

“…For instance, Tomonari Suzuki [25] defined in 2008 a class of generalized nonexpansive mappings, which he called (C)-type mappings, whose setvalued version was defined and studied in [1,2,22,26]. For instance, Tomonari Suzuki [25] defined in 2008 a class of generalized nonexpansive mappings, which he called (C)-type mappings, whose setvalued version was defined and studied in [1,2,22,26].…”

Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)

“…If T : E ! CB(E) is a multivalued nonexpansive mapping, then T satis…es the condition (C) ( [1]). Moreover, if T : E !…”