Vol. 53, No. 1, 1974

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A common fixed point theorem for a commuting family of nonexpansive mappings

Ronald Elroy Bruck, Jr.

Vol. 53 (1974), No. 1, 59–71

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
Received: 6 July 1973
Published: 1 July 1974
Ronald Elroy Bruck, Jr.