On Characterizations of Metric Regularity of Multi-valued Maps

TL;DR

This paper offers a new proof demonstrating that the metric regularity of multi-valued maps can be characterized through the regularity of their contingent variation, extending the concept of contingent derivative.

Contribution

It introduces a novel proof connecting metric regularity with contingent variation, expanding the theoretical understanding of multi-valued maps.

Findings

Metric regularity characterized by contingent variation

Extension of contingent derivative concept

Provides a new proof approach

Abstract

We provide a new proof along the lines of the recent book of A. Ioffe of a 1990's result of H. Frankowska showing that metric regularity of a multi-valued map can be characterized by regularity of its contingent variation - a notion extending contingent derivative.