Table of Contents
Journal of Calculus of Variations
Volume 2013, Article ID 461371, 8 pages
http://dx.doi.org/10.1155/2013/461371
Research Article

Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces

Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh 202002, India

Received 23 March 2013; Accepted 29 April 2013

Academic Editor: Raouf Boucekkine

Copyright © 2013 Shamshad Husain and Sanjeev Gupta. 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

We introduce and study a new system of generalized variational inclusions involving -cocoercive and relaxed -cocoercive operators, which contain the systems of variational inclusions and the systems of variational inequalities, variational inclusions, and variational inequalities as special cases. By using the resolvent technique for the -cocoercive operators, we prove the existence of solutions and the convergence of a new iterative algorithm for this system of variational inclusions in Hilbert spaces. An example is given to justify the main result. Our results can be viewed as a generalization of some known results in the literature.