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doi:10.1016/j.aml.2006.04.025 
Copyright © 2006 Elsevier Ltd All rights reserved.
(A,η)-Accretive mappings and set-valued variational inclusions with relaxed cocoercive mappings in Banach spaces
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Heng-you Lana, 
Received 20 October 2005;
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.
Keywords: (A,η)-Accretive mapping; Resolvent operator technique; Set-valued variational inclusion with relaxed cocoercive mapping; Iterative algorithm; Existence and convergence
Article Outline
- 1. Introduction
- 2. Preliminaries
- 3. (A,η)-Accretive mappings and resolvent operators
- 4. Iterative algorithms and convergence
- References
