Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces

Using Bregman functions, we introduce the new concept of Bregman generalized f-projection operator ProjCf, g:E*→C, where E is a reflexive Banach space with dual space E*; f: E→ℝ∪+∞ is a proper, convex, lower semicontinuous and bounded from below function; g: E→ℝ is a strictly convex and Gâteaux diff...

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Main Authors:	Chin-Tzong Pang, Eskandar Naraghirad, Ching-Feng Wen
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2014/594285

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spelling	doaj-1a14c00d56cf4f6a8005d0489c8581eb2020-11-24T20:58:21ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/594285594285Bregman f-Projection Operator with Applications to Variational Inequalities in Banach SpacesChin-Tzong Pang0Eskandar Naraghirad1Ching-Feng Wen2Department of Information Management, Yuan Ze University, Chung-Li 32003, TaiwanDepartment of Mathematics, Yasouj University, Yasouj 75918, IranCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanUsing Bregman functions, we introduce the new concept of Bregman generalized f-projection operator ProjCf, g:E→C, where E is a reflexive Banach space with dual space E; f: E→ℝ∪+∞ is a proper, convex, lower semicontinuous and bounded from below function; g: E→ℝ is a strictly convex and Gâteaux differentiable function; and C is a nonempty, closed, and convex subset of E. The existence of a solution for a class of variational inequalities in Banach spaces is presented.http://dx.doi.org/10.1155/2014/594285
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen
spellingShingle	Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces Abstract and Applied Analysis
author_facet	Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen
author_sort	Chin-Tzong Pang
title	Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces
title_short	Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces
title_full	Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces
title_fullStr	Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces
title_full_unstemmed	Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces
title_sort	bregman f-projection operator with applications to variational inequalities in banach spaces
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2014-01-01
description	Using Bregman functions, we introduce the new concept of Bregman generalized f-projection operator ProjCf, g:E→C, where E is a reflexive Banach space with dual space E; f: E→ℝ∪+∞ is a proper, convex, lower semicontinuous and bounded from below function; g: E→ℝ is a strictly convex and Gâteaux differentiable function; and C is a nonempty, closed, and convex subset of E. The existence of a solution for a class of variational inequalities in Banach spaces is presented.
url	http://dx.doi.org/10.1155/2014/594285
work_keys_str_mv	AT chintzongpang bregmanfprojectionoperatorwithapplicationstovariationalinequalitiesinbanachspaces AT eskandarnaraghirad bregmanfprojectionoperatorwithapplicationstovariationalinequalitiesinbanachspaces AT chingfengwen bregmanfprojectionoperatorwithapplicationstovariationalinequalitiesinbanachspaces
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Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces

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