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A Typical Nowhere Differentiable Function

Published online by Cambridge University Press:  20 November 2018

F. S. Cater*
Affiliation:
Portland State University Portland, Oregon 97207, U.S.A.
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Garg, K. M., On asymmetrical derivates of non-differentiable functions, Canadian Journal of Mathematics 20, pp. 135143 (1968).CrossRefGoogle Scholar
2. Garg, K. M., On a residual set of continuous functions, Czechoslovak Mathematical Journal 20, pp. 537543 (1970).Google Scholar
3. Jarnik, V., Uber die differenzierbarkeit stetiger funktionen, Fundamenta Mathematicae 21, pp. 4858 (1933).CrossRefGoogle Scholar
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