Real Analysis Exchange

Generalized Kiesswetter’s Functions

Delong Li and Jie Miao

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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.

Article information

Real Anal. Exchange, Volume 40, Number 1 (2015), 141-156.

First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A06: One-variable calculus 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

continuous functions non-differentiable functions


Li, Delong; Miao, Jie. Generalized Kiesswetter’s Functions. Real Anal. Exchange 40 (2015), no. 1, 141--156.

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