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2013 The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems
Lu-Chuan Ceng, Himanshu Gupta, Ching-Feng Wen
Abstr. Appl. Anal. 2013(SI60): 1-19 (2013). DOI: 10.1155/2013/378750

Abstract

The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix ( S ) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of Fix ( S ) Ξ Γ under mild conditions.

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Lu-Chuan Ceng. Himanshu Gupta. Ching-Feng Wen. "The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems." Abstr. Appl. Anal. 2013 (SI60) 1 - 19, 2013. https://doi.org/10.1155/2013/378750

Information

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

zbMATH: 1383.47010
MathSciNet: MR3035321
Digital Object Identifier: 10.1155/2013/378750

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI60 • 2013
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