Abstract and Applied Analysis
Volume 2011 (2011), Article ID 261534, 12 pages
http://dx.doi.org/10.1155/2011/261534
Research Article

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

Rais Ahmad,1 Mohd Dilshad,1 Mu-Ming Wong,2 and Jen-Chin Yao3,4

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, Taiwan
3Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan
4Department of Applied Mathematics, National Sun-Yat Sen University, Kaohsiung 804, Taiwan

Received 15 April 2011; Accepted 25 June 2011

Academic Editor: Ngai-Ching Wong

Copyright © 2011 Rais Ahmad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to introduce a new 𝐻 ( ⋅ , ⋅ ) -cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with 𝐻 ( ⋅ , ⋅ ) -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.