Vol. 80, No. 2, 1979

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Common fixed points and iteration of commuting nonexpansive mappings

Shiro Ishikawa

Vol. 80 (1979), No. 2, 493–501
Abstract

The following result is shown. Let Ti (i = 1,2,) 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

   n∏ν      n∏ν−1        n∏2    ∏n1          ∞
{[      [Sν      [⋅⋅⋅[S3    [S2     S1]]⋅⋅⋅]]]x}nν=1
nν−1=1   nν−2=1       n1=1   n0=1

converges to a common fixed point of {T}i=1ν, where Si = (1αi)I +αiTi, 0 < αi < 1, I is the identity mapping.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 30 May 1978
Published: 1 February 1979
Authors
Shiro Ishikawa