Variational and Generalized Variational Inequalities with Discontinuous Mappings

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Generalized Vector Variational Inequalities with Star-pseudomonotone and Discontinuous Operators

In this paper we deal with the following generalized vector variational inequality problem: let X, Y and Z be topological vector spaces, K be a convex set in X, D be a nonempty set in Y , and C be a closed convex cone in Z. Let T : K → 2 be a multifunction and f : K ×D ×K → Z be a single-valued mapping. Find a point x̂ ∈ K and ŷ ∈ T (x̂) such that f(x̂, ŷ, z) / ∈ −intC, ∀z ∈ K. We prove some exist...

ψ-pseudomonotone generalized strong vector variational inequalities with application

In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.    

Solutions of variational inequalities on fixed points of nonexpansive mappings

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...