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Title: A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
Authors: Narawadee Nanan
Sompong Dhompongsa
Keywords: Mathematics
Issue Date: 1-Jan-2011
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. © 2011 Nanan and Dhompongsa; licensee Springer.
ISSN: 16871812
Appears in Collections:CMUL: Journal Articles

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