Abstract
In this paper, we introduce a new concept of ( A, η)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of ( A, η)-accretive mappings and define resolvent operators associated with ( A, η)-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, η)-accretive mappings and study applications of ( A, η)-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.
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