FIXED POINTS OF LOCAL STRICTLY PSEUDO-CONTRACTIVE MAPPINGS USING MANN AND ISHIKAWA ITERATION WITH ERRORS

摘要

In this paper the concept of the Ishikawa iteration process with errors is introduced and a fixed point of the Lipschitzian local strictly pseudo-contractive mapping is obtained as the limit of an iteratively constructed sequence in uniformly smooth Banach spaces. A related result shows that the Ishikawa iteration process with errors converges strongly to a solution of the equation Tx = f when T is a Lipschitzian local strongly accretive mapping. These results are then used to generalize, improve and unify the corresponding results of Weng, Tan and Xu, Chidume, Osilike and the author in several aspects and to answer, in the more general setting, open questions of Chidume.