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2009 The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces
Rabian Wangkeeree, Rattanaporn Wangkeeree
Abstr. Appl. Anal. 2009: 1-26 (2009). DOI: 10.1155/2009/624798

Abstract

We consider a hybrid projection algorithm based on the shrinking projection method for two families of quasi-ϕ-nonexpansive mappings. We establish strong convergence theorems for approximating the common element of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. As applications, at the end of the paper we first apply our results to consider the problem of finding a zero point of an inverse-strongly monotone operator and we finally utilize our results to study the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.

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Rabian Wangkeeree. Rattanaporn Wangkeeree. "The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces." Abstr. Appl. Anal. 2009 1 - 26, 2009. https://doi.org/10.1155/2009/624798

Information

Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1184.49019
MathSciNet: MR2563998
Digital Object Identifier: 10.1155/2009/624798

Rights: Copyright © 2009 Hindawi

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