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

被引：117

作者：

Lan, Heng-You

Cho, Yeol Je ^{[1
]}

Verma, R. U.

机构：

[1] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[2] Gyeongsang Natl Univ, Coll Educ, RINS, Chinju 660701, South Korea

[3] Sichuan Univ Sci & Engn, Dept Math, Sichuan 643000, Peoples R China

[4] Univ Toledo, Dept Math, Toledo, OH 43606 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2006年 / 51卷 / 9-10期

关键词：

(A; eta)-accretive mapping; resolvent operator technique; nonlinear variational inclusion with relaxed cocoercive mapping; perturbed iterative algorithm with mixed errors; convergence and stability;

D O I：

10.1016/j.camwa.2005.11.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1529 / 1538

页数：10

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