Generalized image-complementarity problems in Banach spaces Original Research Article

In this paper, a class of generalized ff-complementarity problems and three classes of variational inequalities are introduced in real Banach spaces, and the equivalences among them are established under certain conditions. Several coercivity conditions are introduced for the existence of solutions of the generalized ff-complementarity problem. Under some suitable assumptions, it is shown that each of these coercivity conditions is equivalent to the nonemptyness and boundedness of the solution set for the generalized ff-complementarity problem in infinite-dimensional Banach spaces, and even the nonemptyness and compactness of the solution set for the generalized ff-complementarity problem in finite-dimensional spaces. The existence of least elements for the feasible set of the generalized ff-complementarity problem is also presented under suitable conditions.