The generalised f -projection operator with an application

Source abstract

In this paper, we introduce a new concept of generalised f -projection operator which extends the generalised projection operator π K : B * → K , where B is a reflexive Banach space with dual space B * and K is a nonempty, closed and convex subset of B . Some properties of the generalised f -projection operator are given. As an application, we study the existence of solution for a class of variational inequalities in Banach spaces.