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, GSMWVVHIs) and generalized Minty mixed weak vector variational–hemivariational inequalities (in short, GMMWVVHIs) 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 GSMWVVHIs without imposing any monotonicity assumptions on bifunctions and relaxed compactness hypotheses. Moreover, under a generalized, stable pseudomonotonicity hypothesis on bifunctions, we derive an existence theorem for the solutions of GMMWVVHIs and establish an equivalence relation between the solutions of the considered vector variational–hemivariational inequalities. Furthermore, uniqueness results for the solutions of the considered vector variational–hemivariational inequalities are established under suitable assumptions. In addition, we establish the stability of the solution of GSMWVVHIs under some appropriate conditions. We furnish several illustrative examples to demonstrate the significance of the results established in this paper. Finally, we demonstrate that the sustainable electricity generation planning problem can be naturally formulated as a GSMWVVHI.