On continuous functions with no unilateral derivatives (Q1100572)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On continuous functions with no unilateral derivatives |
scientific article; zbMATH DE number 4044123
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On continuous functions with no unilateral derivatives |
scientific article; zbMATH DE number 4044123 |
Statements
On continuous functions with no unilateral derivatives (English)
0 references
1988
0 references
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham's functional equations. Then we show that for any \(\alpha\) \(\in [0,1)\) there exists an \(f_{\alpha}\) in any Lipschitz class of order less than one such that the set of knot points of \(f_{\alpha}\) has a measure \(\alpha\).
0 references
continuous functions on the unit interval which have nowhere a unilateral derivative
0 references
de Rham's functional equations
0 references
set of knot points
0 references
