A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued

Abstract

Bruck [Pac. J. Math. 53, 59-71 1974 Theorem 1] proved that for a nonempty closed convex subset E of a Banach space X, if E is weakly compact or bounded and separable and suppose that E has both (FPP) and (CFPP), then for any commuting family S of nonexpansive self-mappings of E, the set F(S) of common fixed points of S is a nonempty nonexpansive retract of E. In this paper, we extend the above result when one of its elements in S is multivalued. The result extends previously known results (on common fixed points of a pair of single valued and multivalued commuting mappings) to infinite number of mappings and to a wider class of spaces.

Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces

“…To generalized fixed point theory for single valued mapping, studying the corresponding multivalued mappings is constanly developed. See [6,7,8,9,10,11,12,13] for existence theorems and see [14,15,16,17,18,19,20,21] for convergence theorems of fixed point results for both of single valued and multivalued mappings. Recently, many kinds of iterative processes have been used for approximating fixed points of multivalued nonexpansive mappings.…”