Abstract and Applied Analysis

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

Chin-Tzong Pang, Eskandar Naraghirad, and Ching-Feng Wen

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Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 594285, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607611

Digital Object Identifier
doi:10.1155/2014/594285

Mathematical Reviews number (MathSciNet)
MR3186971

Zentralblatt MATH identifier
07022677

Citation

Pang, Chin-Tzong; Naraghirad, Eskandar; Wen, Ching-Feng. Bregman $f$ -Projection Operator with Applications to Variational Inequalities in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 594285, 10 pages. doi:10.1155/2014/594285. https://projecteuclid.org/euclid.aaa/1412607611


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