Common fixed points and iteration of commuting nonexpansive mappings

Shiro Ishikawa

Vol. 80 (1979), No. 2, 493–501

DOI: 10.2140/pjm.1979.80.493

Abstract

The following result is shown. Let T_i (i = 1,2,⋯,ν) be commuting nonexpansive self-mappings on a compact convex subset D of a Banach space and let x be any point in D. Then the sequence

converges to a common fixed point of {T}_i=1^ν, where S_i = (1−α_i)I +α_iT_i, 0 < α_i < 1, I is the identity mapping.

Mathematical Subject Classification 2000

Primary: 47H10

Milestones

Received: 30 May 1978

Published: 1 February 1979