Subdifferential determination of a primal lower regular function on a Banach space

TL;DR

This paper extends a key theorem in convex analysis to Banach spaces, showing that if two primal lower regular functions have identical subdifferentials locally, then they differ only by a constant.

Contribution

It generalizes the Thibault-Zagrodny Theorem from finite-dimensional spaces to Banach spaces, broadening its applicability.

Findings

Established local subdifferential equality implies functions differ by a constant in Banach spaces.

Extended the scope of primal lower regular functions analysis.

Provided a theoretical foundation for further research in convex analysis on Banach spaces.

Abstract

We generalize to Banach space Thibault-Zagrodny Theorem that if $f$ and $g$ are primal lower regular functions and $\partial f = \partial g$ locally, then $f$ and $g$ locally differ by a constant.