(A, η)-accretive mappings and set-valued variational inclusions with relaxed cocoercive mappings in Banach spaces

In this work, we introduce a new concept of (A, eta)-accretive mappings, study some properties of (A, eta)-accretive mappings and define resolvent operators associated with (A, eta)-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, eta)-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. (C) 2006 Elsevier Ltd. All rights reserved.