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Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems

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Abstract

In this paper, we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of asymptotically quasi ϕ-nonexpansive mappings, the set of solutions of variational inequalities and the set of solutions of equilibrium problems in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify the efficiency of the proposed parallel algorithms.

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Acknowledgments

The research of the first author was partially supported by Vietnam Institute for Advanced Study in Mathematics (VIASM) and Vietnam National Foundation for Science and Technology Development (NAFOSTED).

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Correspondence to Pham Ky Anh.

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Dedicated to Professor Nguyen Khoa Son’s 65th birthday.

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Anh, P.K., Van Hieu, D. Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems. Vietnam J. Math. 44, 351–374 (2016). https://doi.org/10.1007/s10013-015-0129-z

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  • DOI: https://doi.org/10.1007/s10013-015-0129-z

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