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Mathematics 2019, 7(4), 338; https://doi.org/10.3390/math7040338

Systems of Variational Inequalities with Nonlinear Operators

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: 2 March 2019 / Revised: 2 April 2019 / Accepted: 3 April 2019 / Published: 9 April 2019
(This article belongs to the Special Issue Variational Inequality)
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PDF [296 KB, uploaded 9 April 2019]

Abstract

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces. View Full-Text
Keywords: implicit iterations; variational inequalities; lipschitzian pseudocontractions; asymptotically nonexpansive mapping; fixed-point; banach space implicit iterations; variational inequalities; lipschitzian pseudocontractions; asymptotically nonexpansive mapping; fixed-point; banach space
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. Systems of Variational Inequalities with Nonlinear Operators. Mathematics 2019, 7, 338.

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