Lineability, differentiable functions and special derivatives

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Fernández Sánchez, Juan and Rodríguez Vidanes, Daniel and Seoane-Sepúlveda, Juan B. and Trutschnig, W. (2021) Lineability, differentiable functions and special derivatives. Banach Journal of Mathematical Analysis, 15 (18). ISSN 1735-8787

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Official URL: https://doi.org/10.1007/s43037-020-00103-9



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: (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.


Item Type:Article
Uncontrolled Keywords:Lineability, Algebrability, Rolle’s theorem, Differentiable function, Derivative
Subjects:Sciences > Mathematics > Algebra
Sciences > Mathematics > Mathematical analysis
ID Code:74694
Deposited On:22 Sep 2022 10:53
Last Modified:22 Sep 2022 12:10

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