Korean J. Math. Vol. 23 No. 3 (2015) pp.457-478
DOI: https://doi.org/10.11568/kjm.2015.23.3.457

A hybrid method for a system involving equilibrium problems, variational inequalities and nonexpansive semigroup

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Published: Sep 30, 2015
Keywords:
fixed point, variational inequality, equilibrium problems, nonexpansive mapping, pseudomonotonicity, semigroup.
Mathematics Subject Classification:
65K10, 65K15, 90C25, 90C33.

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Le Quang Thuy
School of Applied Mathematics and Informatics Hanoi University of Science and Technology No 1, Dai Co Viet Road, Hai Ba Trung, Hanoi, Vietnam
Le Dung Muu
Institute of Mathematics Vietnam Academy of Science and Technology Hanoi, Vietnam

Abstract

In this paper we propose an iteration hybrid method for approximating a point in the intersection of the solution-sets of pseudomonotone equilibrium and variational inequality problems and the fixed points of a semigroup-nonexpensive mappings in Hilbert spaces. The method is a combination of projection, extragradient-Armijo algorithms and Mannís method. We obtain a strong convergence for the sequences generated by the proposed method.


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