On H\"{o}lder exponents of the self-similar functions

TL;DR

This paper investigates the H"{o}lder exponents of affine self-similar functions on [0,1], deriving formulas based on their self-similarity parameters to understand their regularity properties.

Contribution

It provides explicit formulas for H"{o}lder exponents of affine self-similar functions, linking regularity to self-similarity parameters.

Findings

Derived formulas for H"{o}lder exponents in terms of self-similarity parameters

Characterized regularity of affine self-similar functions

Enhanced understanding of function smoothness based on self-similarity

Abstract

We study the class of affine self-similar and continuous on interval $[0;1]$ functions. Formulas for the H\"{o}lder exponents are obtained in terms of self-similarity parameters.