ITERATIVE PROCESS TO STRICTLY PSEUDO-CONTRACTIVE MAPPINGS IN 2-UNIFORMLY SMOOTH
BANACH SPACES

Bao-Hua Guo (P. R. China) and Sheng-Hua Wang (P. R. China)

Received September 21, 2007

Abstract

Let C be a closed convex subset of a 2-uniformly Banach space E with the best smooth constant K and  be a k-strict pseudo-contraction on C with a fixed point, for some  Given an initial guess  consider the Mann’s algorithm    It is proved that if the control sequence  is chosen so that  and  then the Mann iterative sequence  converges weakly to a fixed point of T.

Keywords and phrases: weak convergence, strict pseudo-contractive mapping, fixed point, uniformly smooth Banach spaces.