Vol. 72, No. 1, 1977

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On common fixed points for several continuous affine mappings

Kazuo Anzai and Shiro Ishikawa

Vol. 72 (1977), No. 1, 1–4
Abstract

It is known from Markov-Kakutani theorem that if Tj (j = 1,2,,J) are continuous affine commuting self-mappings on a compact convex subset of a locally convex space, then the intersection of the sets of fixed points of Tf (j = 1,2,,J) is nonempty. The object of this paper is to show a result which says more than the above theorem does, and actually our theorem shows in the case of J = 2 that the set of fixed points of λT1 + (1 λ)T2 always coincides, for each λ(0 < λ < 1), with the intersection of the sets of fixed points of T1 and T2.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 22 December 1976
Revised: 21 March 1977
Published: 1 September 1977
Authors
Kazuo Anzai
Shiro Ishikawa