International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1723-1735
doi:10.1155/IJMMS.2005.1723

Characterizations of fixed points of nonexpansive mappings

Abstract

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.