Using Bregman functions, we introduce the new concept of Bregman generalized -projection operator , where is a reflexive Banach space with dual space is a proper, convex, lower semicontinuous and bounded from below function; is a strictly convex and Gâteaux differentiable function; and is a nonempty, closed, and convex subset of . The existence of a solution for a class of variational inequalities in Banach spaces is presented.
"Bregman -Projection Operator with Applications to Variational Inequalities in Banach Spaces." Abstr. Appl. Anal. 2014 (SI57) 1 - 10, 2014. https://doi.org/10.1155/2014/594285