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

Zhongping Wan | Zendy; Jiawei Chen | Zendy; Hai Sun | Zendy; L. C. L. Yuan | Zendy

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

Author(s) -

Zhongping Wan,

Jiawei Chen,

Hai Sun,

L. C. L. Yuan

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/961038

Subject(s) - hilbert space , convergence (economics) , uniqueness , variational inequality , banach space , mathematics , fixed point , iterative method , fixed point theorem , mathematical optimization , pure mathematics , mathematical analysis , economics , economic growth

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

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