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

Heng-you Lan, Jong Kyu Kim, Zishan Liu

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.

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ISSN: 1229-1595 (Print), 2466-0973 (Online)