Topological stability of continuous functions with respect to averaging by measures with locally constant densities

Sergiy Maksymenko, Oksana Marunkevych

Let $\mu$ be a measure on $[-1,1]$. Then for every continuous function $f:\mathbb{R}\to \mathbb{R}$ and $\alpha >0$ one can define its averaging $f_{\alpha }:\mathbb{R}\to \mathbb{R}$ by the formula…