Regularized gap functions for p-strongly monotone variational-hemivariational inequalities and applications to global error bounds

Abstract

The paper studies regularized gap functions for a general class of elliptic variational–hemivariational inequalities by employing the sum rule of Clarke’s generalized directional derivatives. We first devote regularized gap functions for this class of inequalities based on the forms introduced by Yamashita and Fukushima. Global error bounds for the variational–hemivariational inequality then are formulated in terms of regularized gap functions under strongly monotone assumptions of a general order p > 1 on the given data. The established results are meaningful generalizations to corresponding ones in the literature.