2026-06-28T00:02:35Zhttps://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

00925njm 22002777a 4500 dc Fernández Sánchez, Juan author Rodríguez Vidanes, Daniel Luis author Seoane Sepúlveda, Juan Benigno author Trutschnig, W. author 2021-11-19 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. 1735-8787 10.1007/s43037-020-00103-9 https://hdl.handle.net/20.500.14352/4989 https://doi.org/10.1007/s43037-020-00103-9 Lineability, differentiable functions and special derivatives