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2013 Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces
Lu-Chuan Ceng, Ching-Feng Wen
J. Appl. Math. 2013(SI21): 1-21 (2013). DOI: 10.1155/2013/761864

Abstract

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space. These composite iterative algorithms are based on Korpelevich's extragradient method and viscosity approximation method. We first consider and analyze a composite implicit iterative algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another composite explicit iterative algorithm in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. 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 literatures.

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Lu-Chuan Ceng. Ching-Feng Wen. "Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces." J. Appl. Math. 2013 (SI21) 1 - 21, 2013. https://doi.org/10.1155/2013/761864

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1271.47054
MathSciNet: MR3074340
Digital Object Identifier: 10.1155/2013/761864

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI21 • 2013
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