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

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 operat...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2006-05, Vol.51 (9), p.1529-1538
Hauptverfasser: Lan, Heng-You, Je Cho, Yeol, Verma, R.U.
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Sprache:eng
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Zusammenfassung: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2005.11.036