Formula omitted]-Accretive mappings and set-valued variational inclusions with relaxed cocoercive mappings in Banach spaces

Abstract

In this work, we introduce a new concept of ( A , η ) -accretive mappings, study some properties of ( A , η ) -accretive mappings and define resolvent operators associated with ( A , η ) -accretive mappings which include the existing resolvent operators as special cases. By using the new resolvent operator technique, we also construct a new class of iterative algorithms for a class of relaxed cocoercive variational inclusions involving non-accretive set-valued mappings and study applications of ( A , η ) -accretive mappings to the approximation-solvability of the relaxed cocoercive variational inclusions in q -uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.