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Mathematics 2019, 7(2), 187; https://doi.org/10.3390/math7020187

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

1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
*
Author to whom correspondence should be addressed.
Received: 30 December 2018 / Revised: 2 February 2019 / Accepted: 13 February 2019 / Published: 16 February 2019
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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. View Full-Text
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 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ceng, L.-C.; Yuan, Q. Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems. Mathematics 2019, 7, 187.

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