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Convergence of almost-orbits of nonexpansive semigroups in Banach spaces
Authors:Anthony To-Ming Lau  Koji Nishiura  Wataru Takahashi
Institution:Department of Mathematical and Satistical Sciences, University of Albert, Edmonton, Alberta, Canada T6G 2G1 ; Department of General Education, Fukushima National College of Technology, Taira, Iwaki-shi 970-8034, Japan ; Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract:The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.

Keywords:Mean ergodic theorem  nonexpansive semigroup  almost-orbit  regular net  invariant mean
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