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Fixed point iterations
of nonexpansive mappings
Simeon Reich |
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Vol. 60 (1975), No. 2, 195–198
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Abstract |
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Let C be a boundedly weakly compact convex subset of a Banach space E. Suppose that each weakly compact convex subset of C possesses the fixed point property for nonexpansive mappings, and let T : C → C be nonexpansive. In this note it is shown (by a very simple argument) that if a sequence of iterates of T (generated with the aid of an infinite, lower triangular, regular row-stochastic matrix) is bounded, then T has a fixed point. |
Mathematical Subject Classification 2000
Primary: 47H10
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Milestones
Received: 14 April 1975
Published: 1 October 1975
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Authors |
| Simeon Reich | |
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