One modification of the Salem function

TL;DR

This paper explores a specific modification of the Salem function, analyzing its properties such as functional equations, graph structure, and Lebesgue integrability to understand its mathematical behavior.

Contribution

It introduces a particular modification of the Salem function and investigates its key properties, expanding understanding of Salem-type functions.

Findings

Analysis of the functional equations satisfied by the modified Salem function

Characterization of the graph of the modified Salem function

Assessment of Lebesgue integrability of the modified Salem function

Abstract

The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to functional equations, graphs, the Lebesgue integral, etc.