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doi:10.1016/j.camwa.2005.11.036 
Copyright © 2006 Published by Elsevier Ltd.
Nonlinear relaxed cocoercive variational inclusions involving (A, η)-accretive mappings in banach spaces**
Available online 10 July 2006.
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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.
Keywords: (A, η)-accretive mapping; Resolvent operator technique; Nonlinear variational inclusion with relaxed Cocoercive mapping; Perturbed iterative algorithm with mixed errors; Convergence and stability
