Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces. (2nd June 2013)

• Record Type: Journal Article
• Authors: Husain, Shamshad; Gupta, Sanjeev
• Other Names: Boucekkine Raouf Academic Editor.
• Is Part Of: Journal of calculus of variations. Volume 2013(2013)
• Publication Date: 2013-06-02
• Subjects: Calculus of variations -- Periodicals; Calculus of variations; Electronic journals; Periodicals; 515.64
• DOI: 10.1155/2013/461371
• Languages: English
• ISSNs: 2314-6613

Abstract

Abstract : We introduce and study a new system of generalized variational inclusions involvingH ( ·, · ) -cocoercive and relaxed( p, q ) -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 theH ( ·, · ) -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.