Lineability, differentiable functions and special derivatives

被引：4

作者：

Fernandez-Sanchez, J. ^{[1
]}

Rodriguez-Vidanes, D. L. ^{[2
]}

Seoane-Sepulveda, J. B. ^{[3
]}

Trutschnig, W. ^{[4
]}

机构：

[1] Univ Almeria, Grp Invest Teoria Copulas & Aplicac, Carretera Sacramento S-N, Almeria 04120, Spain

[2] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal & Matemat Aplicada, Plaza Ciencias 3, Madrid 28040, Spain

[3] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal & Matemat Aplicada, Inst Matemat Interdisciplinar IMI, Plaza Ciencias 3, Madrid 28040, Spain

[4] Univ Salzburg, Dept Math, Hellbrunnerstr 34, A-5020 Salzburg, Austria

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2021年 / 15卷 / 01期

关键词：

Lineability; Algebrability; Rolle's theorem; Differentiable function; Derivative; 15A03; 46B87; 26A15; 26A27; 46J10;

D O I：

10.1007/s43037-020-00103-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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: (1) The class of differentiable functions with discontinuous derivative on a set of positive measure, (2) the family of differentiable functions with a bounded, non-Riemann integrable derivative, (3) the family of functions from (0, 1) to R that are not derivatives, or (4) the family of mappings that do not satisfy Rolle's theorem on real infinite dimensional Banach spaces. Several examples and graphics illustrate the obtained results.

引用

页数：22

共 36 条

[1] Linear structure of sets of divergent sequences and series [J].