A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
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.
Anahtar Kelimeler:
Sierpinki Gasket, harmonic function
A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
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,
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- B¨unyamin DEM˙IR, Vakıf DZHAFAROV, S¸ahin KOC¸ AK, Mehmet ¨UREYEN Department of Mathematics, Anadolu University, Eski¸sehir-TURKEY e-mail: bdemir@anadolu.edu.tr e-mail: vcaferov@anadolu.edu.tr e-mail: skocak@anadolu.edu.tr e-mail: mureyen@anadolu.edu.tr
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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