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

Authors :
Lu-Chuan Ceng
Al-Mezel, Saleh A.
Latif, Abdul
Source :
Abstract & Applied Analysis. 2014, p1-18. 18p.
Publication Year :
2014

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10853375
Database :
Academic Search Index
Journal :
Abstract & Applied Analysis
Publication Type :
Academic Journal
Accession number :
100534230
Full Text :
https://doi.org/10.1155/2014/945985