Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T16:08:54.974Z Has data issue: false hasContentIssue false
  • English
  • Français

A Typical Nowhere Differentiable Function

Published online by Cambridge University Press:  20 November 2018

F. S. Cater
F. S. Cater*
Affiliation:
Portland State UniversityPortland, Oregon 97207, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct an explicit continuous function F such that for each point x, every extended real number is a derived number of F at x and F has an infinite left and an infinite right derived number at x.

Keywords

26A2726A15nowhere differentiable functioncontinuous functionDini derivatederived number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 149 - 151
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Garg, K. M., On asymmetrical derivates of non-differentiable functions, Canadian Journal of Mathematics 20, pp. 135–143 (1968).Google Scholar
2. Garg, K. M., On a residual set of continuous functions, Czechoslovak Mathematical Journal 20, pp. 537–543 (1970).Google Scholar
3. Jarnik, V., Uber die differenzierbarkeit stetiger funktionen, Fundamenta Mathematicae 21, pp. 48–58 (1933).Google Scholar