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Fixed Point Theorem and Nonlinear Ergodic Theorem for Nonexpansive Semigroups Without Convexity

Published online by Cambridge University Press:  20 November 2018

Wataru Takahashi
Wataru Takahashi*
Affiliation:
Department of Information Science, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, Japan
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Abstract

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We first prove a nonlinear ergodic theorem for nonexpansive semigroups without convexity in a Hilbert space. Further we prove a fixed point theorem for non-expansive semigroups without convexity which generalizes simultaneously fixed point theorems for left amenable semigroups and left reversible semigroups.

Keywords

Primary: 47A3547H09Fixed pointnonexpansive mappinginvariant meannonlinear ergodic theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 880 - 887
Copyright
Copyright © Canadian Mathematical Society 1992

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