New York Journal of Mathematics
Volume 17 (2011) 569-577


James McCollum

Further notes on a family of continuous, nondifferentiable functions

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Published: September 5, 2011
Keywords: continuous, nowhere differentiable, fractal, Hausdorff dimension, Lebesgue measure, normal number
Subject: 26A30,37C45

We examine a parametrized family of functions Fa, all of which are continuous and some of which are nowhere or almost nowhere differentiable, we explore the behavior of Fa' and Fa'' almost everywhere for different values of a, focusing on specific questions regarding Fa's differentiability for certain a, and we calculate the Hausdorff dimension of the graphs of all Fa.


This work was partially supported by a Michael D. Wilson Scholarship from the University of Maine at Farmington.

Author information

Division of Mathematics and Computer Science, University of Maine at Farmington, Farmington, ME 04938