Solvability Analysis for a Class of Mixed Variational‐Hemivariational Inequalities

This article investigates the existence and uniqueness of solutions to mixed variational‐hemivariational inequalities. Unlike existing approaches in published literature on mixed variational‐hemivariational inequalities, our method for analyzing existence and uniqueness is easy to understand and apply. Moreover, a projection iterative algorithm is provided for solving such inequalities. First, the existence of a solution for an auxiliary hemivariational problem is established. Subsequently, two sequences corresponding to the problem variables are constructed via projection operators. By leveraging the projection theorem and operator properties, the convergence of both sequences is rigorously demonstrated, thereby proving that the limit of the sequences constitutes the unique solution to the mixed variational‐hemivariational inequality. Finally, we provide examples such that satisfy the working hypotheses to illustrate the theory.