H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions-Reference-Cited by-同舟云学术

H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions

Published:2011 Issue: Volume:2011 Page:1-12
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Ahmad Rais¹,Dilshad Mohd¹,Wong Mu-Ming²,Yao Jen-Chin³⁴

Affiliation:

1. Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

2. Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, Taiwan

3. Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan

4. Department of Applied Mathematics, National Sun-Yat Sen University, Kaohsiung 804, Taiwan

Abstract

The purpose of this paper is to introduce a newH(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated withH(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.

Funder

National Sun-Yat Sen University, Taiwan

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2011/261534.pdf

Reference10 articles.

1. Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming

2. Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities

3. H-Monotone operator and resolvent operator technique for variational inclusions