THE EQUIVALENCE BETWEEN THE CONVERGENCES OF MANN AND ISHIKAWA ITERATION METHODS WITH ERRORS FOR DEMICONTINUOUS φ-STRONGLY ACCRETIVE OPERATORS IN UNIFORMLY SMOOTH BANACH SPACES

摘要

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for 0-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.