GAP FUNCTIONS AND ERROR BOUNDS FOR GENERAL SET-VALUED NONLINEAR VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

Abstract

The objective of this article is to study the general set-valued nonlinear variational-hemivariational inequalities and investigate the gap function, regularized gap function and Moreau-Yosida type regularized gap functions for the general set-valued nonlinear variational-hemivariational inequalities, and also discuss the error bounds for such inequalities using the characteristic of the Clarke generalized gradient, locally Lipschitz continuity, inverse strong monotonicity and Hausdorff Lipschitz continuous mappings.