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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 378364, 13 pages
http://dx.doi.org/10.1155/2013/378364
Research Article

-Mixed Cocoercive Operators with an Application for Solving Variational Inclusions in Hilbert Spaces

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

Received 29 May 2013; Accepted 17 September 2013

Academic Editor: William Ziemer

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 investigate a class of new -mixed cocoercive operators in Hilbert spaces. We extend the concept of resolvent operators associated with -cocoercive operators to the -mixed cocoercive operators and prove that the resolvent operator of -mixed cocoercive operator is single valued and Lipschitz continuous. Some examples are given to justify the definition of -mixed cocoercive operators. Further, by using resolvent operator technique, we discuss the approximate solution and suggest an iterative algorithm for the generalized mixed variational inclusions involving -mixed cocoercive operators in Hilbert spaces. We also discuss the convergence criteria for the iterative algorithm under some suitable conditions. Our results can be viewed as a generalization of some known results in the literature.