2026-06-29T02:33:37Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1332752026-02-26T00:47:42Zcom_20.500.14352_14col_20.500.14352_15

Second order differentiability and related topics in the Takagi Class Ferrera Cuesta, Juan Gómez Gil, Javier Llorente Jorge, Jesús In this paper we study some properties concerning the second order differentiability of the functions belonging to the Takagi class as well as the size of the sets where these properties hold. In particular, we characterize the set of points where these functions have a Taylor expansion of order two. Moreover, we also characterize when they satisfy a Stepanov condition of order two at a point. In this context, the convexity of such functions is also investigated. Finally, some interesting examples are provided. 2026-02-25T17:51:37Z 2026-02-25T17:51:37Z 2022 journal article J. Ferrera, J. Gómez Gil, J. Llorente, Second order differentiability and related topics in the Takagi class, Real Anal. Exchange 47 (2022), no. 1, 207–235. 10.14321/realanalexch.47.1.1628458590 https://hdl.handle.net/20.500.14352/133275 https://doi.org/10.14321/realanalexch.47.1.1628458590 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-097286-B-I00/ES/ANALISIS FUNCIONAL NO LINEAL Y GEOMETRICO/ open access Michigan State University Press