Sufficient condition for pseudo-lipschitzian continuity of a family of equalities and inequalities

Abstract

We study the Lipschitz-like properties of multivalued mappings defined by functional parametric equalities and inequalities. Sufficient conditions of pseudo-Lipschitzian continuity are obtained on the basе of the regularity condition of the relaxed constant positive linear dependence (RCPLD) by Andreani et al. The results of the article generalize some known sufficient conditions for pseudo-Lipschitzian continuity of the systems of parametric equalities and inequalities.