Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces. (20th March 2014) - Pang, Chin-Tzong; Naraghirad, Eskandar; Wen, Ching-Feng
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.