On the properties of functions of the Takagi power class

2021/12/15 by O. E. Galkin, Galkin, O. E., S. Yu. Galkina +3
Mathematics · #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2112.08420

openalex publication_date 2021/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By construction, functions of Takagi power class are similar to Takagi's continuous nowhere differentiable function. These functions have one real parameter p>0. They are defined by the series S_p(x) = ∑_n=0^∞ (T₀(2ⁿx)/2ⁿ)^p, where T₀(x) is the distance from the real number x to the nearest integer. We study such properties of functions S_p(x) as continuity, generalized Hölder condition, global maxima and differentiability at the points x=1/3 and x=2/3, for various values of p.

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