On one class of modifications of the Salem function

TL;DR

This paper explores a specific class of functions with complex local structures, modeled by digit operators, extending previous research on their properties and generalizing earlier findings.

Contribution

It introduces a generalization of previous studies on functions with complicated local structures modeled by digit operators.

Findings

Characterization of the properties of the specific class of functions

Extension of earlier results on digit-based operators

Generalization of previous investigations into these functions

Abstract

The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27, 39] and references therein). This research is a generalization of investigations presented in the last-mentioned papers.