A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications
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 e...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/961038 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |