On approximately monotone and approximately Hölder functions

Angshuman R. Goswami, Zsolt Páles

A real valued function $f$ defined on a real open interval $I$ is called $\Phi$-monotone if, for all $x,y\in I$ with $x\le y$ it satisfies $$f(x)\le f(y)+\Phi (y-x),$$ where $Φ:[0,\el…