Error Bound and Hölder Continuity for Parametric Set-valued Variational–Hemivariational Inequalities

In this paper, we are devoted to investigating a parametric set-valued variational–hemivariational inequality (PSVHI), where its data including the constraint set and the involved mappings or functions are perturbed by two independent parameters. By using the Clarke subdifferential of the involved locally Lipschitz continuous function, we introduce a gap function for PSVHI and derive a kind of local continuity for the gap function under the assumption of Hölder continuity for the involved mappings or functions, based on which an error bound result for PSVHI is established under the condition of stable [Formula: see text]-pseudomonotonicity for the involved set-valued mapping. Then, with the assumption of solvability for PSVHI, we prove the Hölder continuity of the set-valued solution mapping of PSVHI with the help of the obtained error bound result and the local continuity for the gap function.