Regularity Modulus of Intersection Mappings. Application to the Stability of Equations via Splitting into Inequalities

This paper is firstly concerned with the modulus of metric regularity of intersection mappings. We consider a finite collection of set-valued mappings and analyze the relationship between the regularity moduli of these mappings (specifically, the maximum of them) and the regularity modulus of the associated intersection mapping. As an application we derive the Lipschitz modulus of the feasible set mapping associated with linear systems of (possibly) infinitely many linear inequalities and finitely many equations. Previously we characterize the metric regularity of such systems. Specifically, we consider an intersection mapping which obeys the strategy of splitting equations into inequalities, and then we apply preliminary results for inequality systems.