Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems
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Authors
Lu-Chuan Ceng
- Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China.
A. Latif
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
A. E. Al-Mazrooei
- Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia.
Abstract
In this paper, we introduce a multi-step iterative algorithm for finding a common element of the set of
solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family
of variational inclusions for maximal monotone and inverse strong monotone mappings, the set of solutions
of general system of variational inequalities and the set of fixed points of a countable family of nonexpansive
mappings in a real Hilbert space. This multi-step iterative algorithm is based on Korpelevich's extragradient
method, viscosity approximation method, projection method, and strongly positive bounded linear
operator and W-mapping approaches. We establish the strong convergence of the sequences generated by
the proposed algorithm to a common element of above mentioned problems under appropriate assumptions,
which also solves some optimization problem. The result presented in this paper improves and extends some
corresponding ones in the earlier and recent literature.
Share and Cite
ISRP Style
Lu-Chuan Ceng, A. Latif, A. E. Al-Mazrooei, Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3397--3423
AMA Style
Ceng Lu-Chuan, Latif A., Al-Mazrooei A. E., Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems. J. Nonlinear Sci. Appl. (2016); 9(5):3397--3423
Chicago/Turabian Style
Ceng, Lu-Chuan, Latif, A., Al-Mazrooei, A. E.. "Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3397--3423
Keywords
- Multi-step iterative algorithm
- mixed equilibrium problem
- Variational inclusion
- nonexpansive mapping
- maximal monotone mapping
- strong convergence.
MSC
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