The radius of metric regularity at infinity

TL;DR

This paper investigates the relationship between metric regularity and its stability at infinity, providing measures of how much perturbation a set-valued mapping can withstand before losing regularity.

Contribution

It introduces relationships at infinity between the modulus of metric regularity and the radius of strong metric regularity, extending existing theorems to the asymptotic setting.

Findings

Established bounds relating metric regularity modulus and stability radius at infinity.

Extended classical theorems to the asymptotic context.

Provided new tools for analyzing stability of set-valued mappings at infinity.

Abstract

This paper, in the setting at infinity, presents some relationships between the modulus of metric regularity and the radius of (strong) metric regularity that gives a measure of the extent to which a set-valued mapping can be perturbed before (strong) metric regularity is lost. The results given here can be viewed as versions at infinity of [2, Theorem 1.5] and [3, Theorem 4.6].