Generalized Kiesswetter's Functions

In 1966, Kiesswetter found an interesting example of continuous everywhere but differentiable nowhere functions using base-4 expansion of real numbers. In this paper we show how Kiesswetter’s function can be extended to general cases. We also provide an equivalent form for such functions via a recur...

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Bibliographic Details
Published inReal analysis exchange Vol. 40; no. 1; pp. 141 - 156
Main Authors Li, Delong, Miao, Jie
Format Journal Article
LanguageEnglish
Published Michigan State University Press 2015
Subjects
26A06
26A15
26A27
continuous functions
non-differentiable functions
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Summary:In 1966, Kiesswetter found an interesting example of continuous everywhere but differentiable nowhere functions using base-4 expansion of real numbers. In this paper we show how Kiesswetter’s function can be extended to general cases. We also provide an equivalent form for such functions via a recurrence relation.
ISSN:0147-1937
1930-1219
DOI:10.14321/realanalexch.40.1.0141