Existence of Solutions for Generalized Mixed Weak Vector Variational-Hemivariational Inequalities

In this paper, we consider the classes of generalized Stampacchia mixed weak vector variational-hemivariational inequalities (in short, GSMWVVHI) and generalized Minty mixed weak vector variational-hemivariational inequalities (in short, GMMWVVHI), formulated in terms of bifunctions. By employing the Knaster-Kuratowski-Mazurkiewicz-Fan (in short, KKM-Fan) lemma, we deduce an existence result for the solutions of GSMWVVHI without imposing any monotonicity assumptions on bifunctions and relaxed compactness hypotheses. Moreover, under generalized stable pseudomonotonicity hypotheses on bifunctions, we derive an existence theorem for the solutions of GMMWVVHI and establish an equivalence relation between the solutions of GSMWVVHI and GMMWVVHI. Furthermore, uniqueness results for the solutions of GSMWVVHI and GMMWVVHI are established under suitable assumptions. Several illustrative examples have been furnished to highlight the applicability and relevance of the established results. To the best of our knowledge, existence and uniqueness results for solutions of GSMWVVHI and GMMWVVHI have been established for the first time in this paper on the Euclidean spaces.