Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems
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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.
KeywordsAsymptotically quasi ϕ-nonexpansive mapping Variational inequality Equilibrium problem Hybrid method Parallel computation
Mathematics Subject Classification (2010)47H05 47H09 47H10 47J25 65J15 65Y05
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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