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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th-cmuir.6653943832-431172017-09-28T06:48:19Z A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued Nanan N. Dhompongsa S. 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. 2017-09-28T06:48:19Z 2017-09-28T06:48:19Z 2011-01-01 Journal 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/6653943832/43117 |
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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 |
Nanan N. Dhompongsa S. |
| spellingShingle |
Nanan N. Dhompongsa S. A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued |
| author_facet |
Nanan N. Dhompongsa S. |
| author_sort |
Nanan N. |
| 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 |
2017 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84873054258&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43117 |
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