On the differentiability of certain saltus functions

• Autorzy: Gerald Kuba
• Języki publikacji: EN

Abstrakty

EN

We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f'(ξ) = 0 if f'(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that $g'(x) = 2^{x}$ for all rational numbers x and g'(x) = 0 for almost all irrational numbers x.

Kategorie tematyczne

• 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
• 26A06: One-variable calculus
• 26A30: Singular functions, Cantor functions, functions with other special properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 1
• Strony: 15-30

Daty

wydano

2011

Twórcy

autor

Gerald Kuba

• Institute of Mathematics, University of Natural Resources and Life Sciences, Wien, Austria

Identyfikatory

DOI

10.4064/cm125-1-3