Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces. (20th March 2014)

• Record Type: Journal Article
• Authors: Pang, Chin-Tzong; Naraghirad, Eskandar; Wen, Ching-Feng
• Other Names: Yao Jen-Chih Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/594285
• Languages: English
• ISSNs: 1085-3375

Abstract

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 → 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.