Mann iteration of weak convergence theorems in Banach space

In this paper, by using Mann’s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich’s theorem from nonexpansive mappings to k-strict pseudocontractive mappings. Supported by National Science Foundation of China (60872095), the Natural Science Foundation of Zhejiang Province (Y606093), K.C. Wong Magna Fund in Ningbo University and Ningbo Natural Science Foundation (2008A610018).