Abstract and Applied Analysis

Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces

Lu-Chuan Ceng, Saleh A. Al-Mezel, and Abdul Latif

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Abstract

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich’s extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in X, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 945985, 18 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606247

Digital Object Identifier
doi:10.1155/2014/945985

Mathematical Reviews number (MathSciNet)
MR3173298

Zentralblatt MATH identifier
07023368

Citation

Ceng, Lu-Chuan; Al-Mezel, Saleh A.; Latif, Abdul. Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 945985, 18 pages. doi:10.1155/2014/945985. https://projecteuclid.org/euclid.aaa/1412606247


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