Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Lu-Chuan Ceng and Qing Yuan
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Qing Yuan: School of Mathematics and Statistics, Linyi University, Linyi 276000, China

Mathematics, 2019, vol. 7, issue 2, 1-19

Abstract: In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

Keywords: multiple hybrid implicit iteration method; triple hierarchical constrained variational inequality; general system of variational inequalities; fixed point; asymptotically nonexpansive mapping; pseudocontractive mapping; strong convergence; Hilbert spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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