In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

The paper studies three classes of optimization problems with bilevel structure including mathematical programs with equilibrium constraints (MPEC) and semiinfinite problems (SIP). The main goal of the paper is to provide results which establish the existence of feasible points of the problems. These results are based on the so-called KKM Lemma. We are also interested in the convexity propertie...

We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces.We use Fan-KKM lemma and concept of η-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalit...

Using the KKM technique, we establish some existence results for variationalhemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several sufficient conditions for the existence of solutions in the case of unbounded subsets.