Well‐posedness for a Class of Variational–Hemivariational Inequalities with Perturbations

In this paper, we consider an extension of well‐posedness for a minimization problem to a class of variational–hemivariational inequalities with perturbations. We establish some metric characterizations for the well‐posed variational–hemivariational inequality and give some conditions under which the variational–hemivariational inequality is strongly well‐posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well‐posedness of variational–hemivariational inequality and the well‐posedness of corresponding inclusion problem.