Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations

Abstract

The purpose of this paper is to revise the definitions of Ishikawa and Mann iterative processes with errors, by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationTx=fand the convergence problem of Ishikawa and Mann iterative sequences for strongly pseudo-contractive mappings without the Lipschitz condition. The results presented in this paper improve and extend the corresponding results in [4,5,7-10,12,15,16] in the more general setting. In particular, the open problem mentioned by Chidume in [5] has been given an affirmative answer. © 1998 Academic Press.