Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces - Chin-Tzong Pang; Eskandar Naraghirad; Ching-Feng Wen (Abstract and Applied Analysis)
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.