NONLINEAR QUASI-VARIATIONAL INCLUSIONS INVOLVING GENERALIZED m-ACCRETIVE MAPPINGS

Abstract

We consider a new class of nonlinear quasi-variational inclusions involving generalized m-accretive mappings in Banach spaces. By using the Nadler's theorem and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we construct some new iterative algorithms for finding the approximate solutions of this class of nonlinear quasi-variational inclusions in Banach spaces. We also establish that the iterative sequences obtained by the algorithms converge to the exact solution of the nonlinear quasi-variational inclusions involving generalized m-accretive mappings in q-uniformly smooth Banach spaces.