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

An example for a one-parameter nonexpansive semigroup

Tomonari Suzuki

 Department of Mathematics, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan
Received 20 December 2003

Abstract

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