On the Hölder continuity of certain functions
type: Item
instance of: scholarly article
title: On the Hölder continuity of certain functions
zbMATH Open document ID: 0726.26001
author: Abdullah Shidfar
author: Kazem Sabetfakhri
published in: Expositiones Mathematicae
publication date: 1990-01-01T00:00:00Z
review text: The authors prove a theorem giving some sufficient conditions under which a real function of the form \(f(x)=\sum^{\infty}_{n=0}f_ n(x)\) is Hölder continuous. The Hölder continuity of the van der Waerden's function \(f(x)=\sum^{\infty}_{n=0}2^{-n}d(2^ nx,{\mathbb{Z}})\) and of the Weierstrass' functions \(f(x)=\sum^{\infty}_{n=0}a^ n \cos b^ n\pi x,\quad 0<a<1,\quad ab\geq 1,\) is obtained as a corollary of the theorem.
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 4198359
zbMATH Keywords: Hölder continuity
zbMATH Keywords: van der Waerden's function
zbMATH Keywords: Weierstrass' functions
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4198359