Iterative processes with errors for nonlinear equations

Abstract

In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators. Our results generalise, improve, and extend several recent results.