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Abstract and Applied Analysis
Volume 2005, Issue 2, Pages 173-183
http://dx.doi.org/10.1155/AAA.2005.173

An example for a one-parameter nonexpansive semigroup

Department of Mathematics, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan

Received 20 December 2003

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give one example for a one-parameter nonexpansive semigroup. This example shows that there exists a one-parameter nonexpansive semigroup {T(t):t0} on a closed convex subset C of a Banach space E such that limt(1/t)0tT(s)xdsx=0 for some xC, which is not a common fixed point of {T(t):t0}.