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2013 Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m -Accretive Operators in Banach Spaces
Lu-Chuan Ceng, Ching-Feng Wen
Abstr. Appl. Anal. 2013(SI09): 1-21 (2013). DOI: 10.1155/2013/852760

Abstract

The purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being also zeros of an m -accretive operator A in the setting of real uniformly convex and 2-uniformly smooth Banach space X . Here the modified hybrid steepest-descent methods are based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descent algorithms for finding a common element of the solution set of the GSVI and the set A - 1 ( 0 ) of zeros of A in X . Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

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Lu-Chuan Ceng. Ching-Feng Wen. "Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m -Accretive Operators in Banach Spaces." Abstr. Appl. Anal. 2013 (SI09) 1 - 21, 2013. https://doi.org/10.1155/2013/852760

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095433
MathSciNet: MR3096816
Digital Object Identifier: 10.1155/2013/852760

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI09 • 2013
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