## Abstract and Applied Analysis

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

#### Abstract

Using Bregman functions, we introduce the new concept of Bregman generalized $f$-projection operator ${\text{Proj}}_{C}^{f, g}:{E}^{\ast}\to C$, where $E$ is a reflexive Banach space with dual space ${E}^{\ast}; f: E\to \Bbb R\cup \{+\infty \}$ is a proper, convex, lower semicontinuous and bounded from below function; $g: E\to \Bbb R$ 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.

#### 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

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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