On multivalued nonlinear variational inclusion problems with ( A,η)-accretive mappings in Banach spaces

Abstract

Based on the notion of ( A,η)-accretive mappings and the resolvent operators associated with ( A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with ( A,η)-accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving ( A,η)-accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in q-uniformly smooth Banach spaces.