An existence result for a mixed variational problem arising from Contact Mechanics

We consider a mixed variational problem involving a nonlinear, hemicontinuous, generalized monotone operator. The proposed problem consists of a variational equation in a real reflexive Banach space and a variational inequality in a subset of a second real reflexive Banach space. We investigate the existence of the solution using a fixed point theorem for set valued mapping. An example arising from Contact Mechanics illustrates the theory.