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

Abstract EN

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.