Vol. 60, No. 2, 1975

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Fixed point iterations of nonexpansive mappings

Simeon Reich

Vol. 60 (1975), No. 2, 195–198

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
Received: 14 April 1975
Published: 1 October 1975
Simeon Reich