Path derived numbers and path derivatives of continuous functions with respect to continuous systems of paths

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

V. Jarnik showed that a typical continuous function on the unit interval [0, 1] has every extended real number as a derived number at every point of [0, 1]. In this paper we classify the derived numbers of a continuous function and study the likelihood of Jarnik's Theorem for path derived numbers of a continuous system of paths. We also provide some results indicating that some of the nice behaviors of first return derivatives are shared by path derivatives of continuous functions when the path system is continuous.

Original languageEnglish (US)
Pages (from-to)355-364
Number of pages10
JournalReal Analysis Exchange
Volume29
Issue number1
DOIs
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Path derived numbers and path derivatives of continuous functions with respect to continuous systems of paths'. Together they form a unique fingerprint.

  • Cite this