Linear regularity, equirregularity, and intersection mappings for convex semi-infinite inequality systems

In this paper, we introduce the concepts of linear regularity and equirregularity for an arbitary family of set-valued mappings between (extended) metric spaces. The concept of linear regularity is inspired in the same property for a family of sets. Then we analyze the relationship between the (metric) regularity moduli of the mappings in the family and the modulus of the associated intersection mapping. We are particularly concerned with the solution set of a system of infinitely many convex inequalities. Our framework allows for right hand side perturbations as well as for linear perturbations of the left hand side of all the inequalities.