The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuousφ-strongly accretive operators in uniformly smooth Banach spaces

Abstract

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuousφ-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 forφ-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.