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Mathematics 2019, 7(3), 218; https://doi.org/10.3390/math7030218

Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2
Department of Mathematics, Ren’ai College, Tianjin University, Tianjin 301636, China
*
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 19 February 2019 / Accepted: 21 February 2019 / Published: 26 February 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Full-Text   |   PDF [280 KB, uploaded 26 February 2019]

Abstract

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions. View Full-Text
Keywords: mann-type implicit iteration methods; triple hierarchical constrained variational inequality; general system of variational inequalities; strong convergence; hilbert spaces mann-type implicit iteration methods; triple hierarchical constrained variational inequality; general system of variational inequalities; 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.; Yang, X. Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems. Mathematics 2019, 7, 218.

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