A simple proof of the rationality of Takagi-like functions

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-11-04 DOI:10.1007/s00010-024-01134-5

Yangyang Chen, Nankun Hong, Hongyuan Yu

引用次数: 0

Abstract

Takagi function is a well-known continuous but nowhere differentiable function defined over real numbers. The Takagi function maps rational numbers to themselves. In this note, by applying Euler’s theorem, we give a simple proof of this property for Takagi-like functions, a slight generalization of the Takagi function.

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高木类函数合理性的简单证明

Takagi函数是一个众所周知的连续但无处可微的实数函数。Takagi函数将有理数映射到自身。本文应用欧拉定理，对Takagi类函数的这一性质作了简单的证明，这是Takagi函数的一个轻微推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.