International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1723-1735
Characterizations of fixed points of nonexpansive mappings
Department of Mathematics, Kyushu Institute of Technology, Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan
Received 14 September 2004; Revised 24 March 2005
Copyright © 2005 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.
Using the notion of Banach limits, we discuss the characterization
of fixed points of nonexpansive mappings in Banach spaces. Indeed, we prove that the two sets of fixed points of a nonexpansive mapping and some mapping generated by a Banach limit coincide. In our discussion, we may not assume the strict convexity of the Banach space.