The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption

Abstract

In this paper we prove some new equivalences between convergence of the Ishikawa and Mann iteration sequences with errors in two schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91–101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114–125], respectively, for strongly successively pseudocontractive mappings. Our main results improve and extend the corresponding results of the all references listed in this article.