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

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 comm...

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Main Authors:	Narawadee Nanan, Sompong Dhompongsa
Format:	Journal
Published:	2018
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84873054258&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50134
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-501342018-09-04T04:24:52Z A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued Narawadee Nanan Sompong Dhompongsa Mathematics 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. 2018-09-04T04:24:52Z 2018-09-04T04:24:52Z 2011-01-01 Journal 16871812 16871820 2-s2.0-84873054258 10.1186/1687-1812-2011-54 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84873054258&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50134
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Narawadee Nanan Sompong Dhompongsa A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
description	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.
format	Journal
author	Narawadee Nanan Sompong Dhompongsa
author_facet	Narawadee Nanan Sompong Dhompongsa
author_sort	Narawadee Nanan
title	A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
title_short	A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
title_full	A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
title_fullStr	A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
title_full_unstemmed	A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
title_sort	common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84873054258&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50134
_version_	1681423535153610752

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

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