Journal of Applied Mathematics

A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications

Zhongping Wan, Jia-Wei Chen, Hai Sun, and Liuyang Yuan

Full-text: Open access

Abstract

A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorithms for solving the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover, strong convergence theorems of these iterative sequences generated by the corresponding algorithms are proved under suitable conditions. As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main results in this paper develop, improve, and unify some well-known results in the literature.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 961038, 26 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818631

Digital Object Identifier
doi:10.1155/2011/961038

Mathematical Reviews number (MathSciNet)
MR2830755

Zentralblatt MATH identifier
1296.47063

Citation

Wan, Zhongping; Chen, Jia-Wei; Sun, Hai; Yuan, Liuyang. A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications. J. Appl. Math. 2011 (2011), Article ID 961038, 26 pages. doi:10.1155/2011/961038. https://projecteuclid.org/euclid.jam/1331818631


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