A PROPERTY OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

Abstract

By suing the famous Banach's fixed point theorem and the concept of uniformly convex,this paper proves that if X is a Hilbert space, C is a closed convex sunset of X, T:C->C a non-expansive mapping, then the limit of (1/n)T^nx must be exist for all x in C, and equals to the limit of uxu (u->0+), where xu is the fixed point of the mapping T/(1+u) (u > 0) in C.