2020
DOI: 10.1007/s43037-020-00103-9
|View full text |Cite
|
Sign up to set email alerts
|

Lineability, differentiable functions and special derivatives

Abstract: The present work either extends or improves several results on lineability of differentiable functions and derivatives enjoying certain special properties. Among many other results, we show that there exist large algebraic structures inside the following sets of special functions: (i.-) The class of differentiable functions with discontinuous derivative on a set of positive measure, (ii.-) the family of differentiable functions with a bounded, non-Riemann integrable derivative, (iii.-) the family of functions … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
5
0

Year Published

2022
2022
2022
2022

Publication Types

Select...
3

Relationship

2
1

Authors

Journals

citations
Cited by 3 publications
(5 citation statements)
references
References 30 publications
0
5
0
Order By: Relevance
“…analogously to f the new operator ˆ f is well-defined, linear, injective, and Lipschitz continuous with Lipschitz constant L = 1 (but not an isometry). Using ˆ f we can show the subsequent result (Theorem 2.3 combined with Corollary 2.1 in [18])-thereby D dis denotes the set of all functions h ∈ C([0, 1]) which are differentiable on [0, 1] (at 0 and 1 we consider the one-sided derivates) with a derivative that is discontinuous at every point of a set with positive λ-measure, and D ¬R the family of all functions h ∈ C([0, 1]) which are differentiable on [0, 1] with a derivative that is bounded but not Riemann integrable.…”
Section: Focusing Exclusively On the Hausdorff Dimension Working Withmentioning
confidence: 87%
See 3 more Smart Citations
“…analogously to f the new operator ˆ f is well-defined, linear, injective, and Lipschitz continuous with Lipschitz constant L = 1 (but not an isometry). Using ˆ f we can show the subsequent result (Theorem 2.3 combined with Corollary 2.1 in [18])-thereby D dis denotes the set of all functions h ∈ C([0, 1]) which are differentiable on [0, 1] (at 0 and 1 we consider the one-sided derivates) with a derivative that is discontinuous at every point of a set with positive λ-measure, and D ¬R the family of all functions h ∈ C([0, 1]) which are differentiable on [0, 1] with a derivative that is bounded but not Riemann integrable.…”
Section: Focusing Exclusively On the Hausdorff Dimension Working Withmentioning
confidence: 87%
“…Considering yet another small modification of f allows for quick alternative proofs for some of the results going back to [18,19]. In fact, setting…”
Section: Focusing Exclusively On the Hausdorff Dimension Working Withmentioning
confidence: 99%
See 2 more Smart Citations
“…For instance, we can name algebrability and strong algebrability defined in [5,8], respectively. We refer the interested reader to [1,2,[4][5][6][10][11][12][13][14][14][15][16][17][19][20][21][22]24,25,[27][28][29]45] for a current state of the art on this topic.…”
Section: Introductionmentioning
confidence: 99%