Real Analysis Exchange

Constructing nowhere differentiable functions from convex functions.

F. S. Cater

Full-text: Open access

Abstract

We find an easy way to construct a continuous nowhere differentiable function from any nondecreasing convex function mapping the unit interval onto itself. We give a number of examples of nowhere differentiable functions constructed this way.

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 617-623.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963822

Mathematical Reviews number (MathSciNet)
MR2010342

Zentralblatt MATH identifier
1063.26003

Subjects
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A51: Convexity, generalizations

Keywords
finite derivative nowhere differentiable convex concave

Citation

Cater, F. S. Constructing nowhere differentiable functions from convex functions. Real Anal. Exchange 28 (2002), no. 2, 617--623. https://projecteuclid.org/euclid.rae/1184963822


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