Characterizations of directional openness for set-valued mappings

TL;DR

This paper establishes necessary and sufficient conditions for directional openness of set-valued mappings in finite-dimensional spaces, linking it with regularity, inverse continuity, coderivatives, and variations.

Contribution

It generalizes and refines existing results by providing a comprehensive characterization of directional openness in set-valued mappings.

Findings

Characterizes directional openness via regularity and inverse properties

Relates directional openness to coderivatives and variations

Provides refined conditions extending previous results

Abstract

We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regularity, H\"older continuity of the inverse mapping, coderivatives and variations. These generalize and refine some previously known results.