A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set

Authors

BÜNYAMİN DEMİR
VAKIF DZHAFAROV
ŞAHİN KOÇAK
MEHMET ÜREYEN

DOI

-

Abstract

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on another dense set. Although such examples could be constructed by classical means of probability and measure theory, this one is more elementary and emerges naturally as a byproduct of some new fractal constructions.

Keywords

Sierpinki Gasket, harmonic function

First Page

211

Last Page

220

Recommended Citation

DEMİR, BÜNYAMİN; DZHAFAROV, VAKIF; KOÇAK, ŞAHİN; and ÜREYEN, MEHMET (2006) "A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set," Turkish Journal of Mathematics: Vol. 30: No. 2, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol30/iss2/7