2026-08-20T15:35:17Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/49892025-04-08T14:38:01Zcom_20.500.14352_14col_20.500.14352_15

Lineability, differentiable functions and special derivatives Fernández Sánchez, Juan Rodríguez Vidanes, Daniel Luis Seoane Sepúlveda, Juan Benigno Trutschnig, W. 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. 2023-06-16T14:25:16Z 2023-06-16T14:25:16Z 2023-06-16T14:25:16Z 2021-11-19 journal article https://hdl.handle.net/20.500.14352/4989 1735-8787 10.1007/s43037-020-00103-9 eng PGC2018-097286-B-I00 open access Springer