# Subdifferential stability and subdifferential sum rules

## TL;DR

This paper investigates the stability properties of subdifferentials and strong slopes of lower semicontinuous functions under Wijsman perturbations, and relates subdifferential sum rules to these stability results.

## Contribution

It provides new insights into the stability of subdifferentials under Wijsman convergence and unifies subdifferential sum rules within this stability framework.

## Key findings

- Subdifferentials are stable under Wijsman perturbations.
- Subdifferential sum rules are special cases of stability results.
- The paper establishes conditions for stability of the strong slope.

## Abstract

In the first part, we discuss the stability of the strong slope and of the subdifferential of a lower semicontinuous function with respect to Wijsman perturbations of the function, i.e. perturbations described via Wijsman convergence. In the second part, we show how subdifferential sum rules can be viewed as special cases of subdifferential stability results.