Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems

Lu-Chuan Ceng and Meijuan Shang
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Meijuan Shang: College of Science, Shijiazhuang University, Shijiazhuang 266100, China

Mathematics, 2019, vol. 7, issue 10, 1-18

Abstract: In this work, let X be Banach space with a uniformly convex and q -uniformly smooth structure, where 1 < q ≤ 2 . We introduce and consider a generalized Mann-like viscosity implicit rule for treating a general optimization system of variational inequalities, a variational inclusion and a common fixed point problem of a countable family of nonexpansive mappings in X . The generalized Mann-like viscosity implicit rule investigated in this work is based on the Korpelevich’s extragradient technique, the implicit viscosity iterative method and the Mann’s iteration method. We show that the iterative sequences governed by our generalized Mann-like viscosity implicit rule converges strongly to a solution of the general optimization system.

Keywords: generalized Mann-like viscosity rule; system of variational inequalities; variational inclusions; nonexpansive mappings; strong convergence; uniform convexity; uniform smoothness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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