Nonlinear relaxed cocoercive variational inclusions involving (A, η)-accretive mappings in Banach spaces

In this paper, we introduce a new concept of (A, eta)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of (A, eta)-accretive mappings and define resolvent operators associated with (A, eta)-accretive mappings. By using the new resolvent operator technique, we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving (A, eta)-accretive mappings and study applications of (A,eta)-accretive mappings to the approximation-solvability of this class of nonlinear relaxed cocoercive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works. (c) 2006 Elsevier Ltd. All rights reserved.