Topological stability of continuous functions with respect to averagings

TL;DR

This paper establishes conditions under which continuous functions with finitely many local extrema remain topologically stable when averaged by discrete measures with finite supports.

Contribution

It provides new sufficient conditions for the topological stability of such functions under averaging operations.

Findings

Identifies conditions ensuring stability under averaging.

Applies to functions with finitely many local extrema.

Advances understanding of stability in topological function analysis.

Abstract

We present sufficient conditions for topological stability of continuous functions $f:\mathbb{R}\to\mathbb{R}$ having finitely many local extrema with respect to averagings by discrete measures with finite supports.