Abstract and Applied Analysis
Volume 2006 (2006), Article ID 58684, 10 pages
Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces
Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
Received 20 December 2003; Accepted 10 July 2005
Copyright © 2006 Tomonari Suzuki. 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.
One of our main results is the following convergence
theorem for one-parameter nonexpansive semigroups: let be a bounded closed convex subset of a Hilbert space , and let be a strongly continuous semigroup of nonexpansive mappings on . Fix and with . Define a sequence in by for , where is a sequence in converging to . Then converges strongly to a common fixed point of .