Geodesic
On the differentiability of certain saltus functions
Gerald Kuba1
1 Institute of Mathematics University of Natural Resources and Life Sciences Wien, Austria
Colloquium Mathematicum, Tome 125 (2011) no. 1, pp. 15-30.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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'(\xi )=0$ if $ f'(\xi )$ 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 $x$.
DOI : 10.4064/cm125-1-3
Keywords: investigate several natural questions differentiability certain strictly increasing singular functions furthermore motivated observation each famous singular function investigated past exists finite example increasing real function constructed rational numbers almost irrational numbers

Gerald Kuba 1

1 Institute of Mathematics University of Natural Resources and Life Sciences Wien, Austria 
@article{10_4064_cm125_1_3,
     author = {Gerald Kuba},
     title = {On the differentiability of certain
 saltus functions},
     journal = {Colloquium Mathematicum},
     pages = {15--30},
     publisher = {mathdoc},
     volume = {125},
     number = {1},
     year = {2011},
     doi = {10.4064/cm125-1-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm125-1-3/}
}
TY  - JOUR
AU  - Gerald Kuba
TI  - On the differentiability of certain
 saltus functions
JO  - Colloquium Mathematicum
PY  - 2011
SP  - 15
EP  - 30
VL  - 125
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm125-1-3/
DO  - 10.4064/cm125-1-3
LA  - en
ID  - 10_4064_cm125_1_3
ER  - 
%0 Journal Article
%A Gerald Kuba
%T On the differentiability of certain
 saltus functions
%J Colloquium Mathematicum
%D 2011
%P 15-30
%V 125
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm125-1-3/
%R 10.4064/cm125-1-3
%G en
%F 10_4064_cm125_1_3
Gerald Kuba. On the differentiability of certain
 saltus functions. Colloquium Mathematicum, Tome 125 (2011) no. 1, pp. 15-30. doi : 10.4064/cm125-1-3. http://geodesic.mathdoc.fr/articles/10.4064/cm125-1-3/

Cité par Sources :