STABLE PERTURBED ITERATION PROCEDURES FOR SOLVING NEW STRONGLY NONLINEAR OPERATOR INCLUSIONS IN BANACH SPACES

Abstract

The purpose of this paper is to introduce and study a new kind of strongly non-linear operator inclusions involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique associated with the generalized m-accretive mappingdue to Huang and Fang, we prove the existence theorems of the solution for this kind of operator inclusions in Banach spaces, and discuss the convergence and stability of a new perturbed iterative algorithm with mixed errors for solving this class of nonlinear operator inclusions in Banach spaces. Our results improve and generalize the corresponding results of recent works.