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2013 Hybrid Extragradient Methods for Finding Zeros of Accretive Operators and Solving Variational Inequality and Fixed Point Problems in Banach Spaces
Lu-Chuan Ceng, Ching-Feng Wen
Abstr. Appl. Anal. 2013(SI45): 1-27 (2013). DOI: 10.1155/2013/894926

Abstract

We introduce and analyze hybrid implicit and explicit extragradient methods for finding a zero of an accretive operator and solving a general system of variational inequalities and a fixed point problem of an infinite family of nonexpansive self-mappings in a uniformly convex Banach space X which has a uniformly Gateaux differentiable norm. We establish some strong convergence theorems for hybrid implicit and explicit extra-gradient algorithms under suitable assumptions. Furthermore, we derive the strong convergence of hybrid implicit and explicit extragradient algorithms for finding a common element of the set of zeros of an accretive operator and the common fixed point set of an infinite family of nonexpansive self-mappings and a self-mapping whose complement is strictly pseudocontractive and strongly accretive in X . 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. "Hybrid Extragradient Methods for Finding Zeros of Accretive Operators and Solving Variational Inequality and Fixed Point Problems in Banach Spaces." Abstr. Appl. Anal. 2013 (SI45) 1 - 27, 2013. https://doi.org/10.1155/2013/894926

Information

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

zbMATH: 07095470
MathSciNet: MR3108488
Digital Object Identifier: 10.1155/2013/894926

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI45 • 2013
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