Systems of Variational Inequalities with Nonlinear Operators

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 4, 1-20

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.

Keywords: implicit iterations; variational inequalities; lipschitzian pseudocontractions; asymptotically nonexpansive mapping; fixed-point; banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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