# On Lipschitz-like continuity of a class of set-valued mappings

## TL;DR

This paper investigates the Lipschitz-like continuity of set-valued mappings derived from parametric systems of equalities and inequalities, establishing conditions under relaxed constraint qualifications.

## Contribution

It introduces new conditions for Lipschitz-like continuity of set-valued mappings based on relaxed constant rank constraint qualification.

## Key findings

- Lipschitz-like continuity holds under relaxed conditions
- Provides theoretical framework for parametric systems
- Extends previous results with weaker assumptions

## Abstract

We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed constant rank constraint qualification.