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A
common fixed point theorem for a commuting family of
nonexpansive mappings
Ronald Elroy Bruck, Jr. |
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Vol. 53 (1974), No. 1, 59–71
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Abstract |
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It is shown that if a closed convex subset C of a Banach space has both the fixed point property and the conditional fixed point property for nonexpansive mappings and C is either weakly compact or bounded and separable, then any commuting family of nonexpansive self-mappings of C has a common fixed point. The set of common fixed points is a nonexpansive retract of C. |
Mathematical Subject Classification 2000
Primary: 47H10
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Milestones
Received: 6 July 1973
Published: 1 July 1974
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Authors |
| Ronald Elroy Bruck, Jr. | |
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