Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions
Keyword(s):
We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.
2009 ◽
Vol 3
(4)
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pp. 605-614
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2012 ◽
Vol 157
(3)
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pp. 781-802
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2009 ◽
Vol 46
(5)
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pp. 885-894
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2008 ◽
Vol 48
(11)
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pp. 1927-1935