Nowhere monotone and Cantor functions
type: Item
instance of: scholarly article
title: Nowhere monotone and Cantor functions
zbMATH Open document ID: 0637.26005
author: Togo Nishiura
author: E. E. Posey
author: Jerry E. Vaughan
published in: Real Analysis Exchange
publication date: 1987-01-01T00:00:00Z
review text: For f: [a,b]\(\to R\) let \(\alpha [f](t)=\sup f([a,t])\), \(t\in [a,b]\), be called the associate of f. A continuous function \(f: [a,b]\to R\) is called a Cantor function when its set of constancy \(K(f)=\{x\in [a,b]:\) f is constant on some neighborhood of \(x\}\) is a dense, proper subset of \([a,b].\) In this paper the authors investigate some properties differentiability properties) of associates of continuous functions, the class of differentiable Cantor functions and the relationship between Cantor functions and the monotone-light factorization of continuous functions.
Mathematics Subject Classification ID: 26A30
Mathematics Subject Classification ID: 26A24
zbMATH DE Number: 4038127
zbMATH Keywords: nowhere monotone function
zbMATH Keywords: differentiability properties
zbMATH Keywords: associates of continuous functions
zbMATH Keywords: Cantor functions
zbMATH Keywords: monotone-light factorization
reviewed by: Zbigniew Grande
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4038127