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2022 Second Order Differentiability and related topics in the Takagi Class
Juan Ferrera, Javier Gómez Gil, Jesús Llorente
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Real Anal. Exchange 47(1): 207-236 (2022). DOI: 10.14321/realanalexch.47.1.1628458590

Abstract

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.

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Juan Ferrera. Javier Gómez Gil. Jesús Llorente. "Second Order Differentiability and related topics in the Takagi Class." Real Anal. Exchange 47 (1) 207 - 236, 2022. https://doi.org/10.14321/realanalexch.47.1.1628458590

Information

Published: 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.14321/realanalexch.47.1.1628458590

Subjects:
Primary: 26A24 , 26A30 , 26A45 , 26A51‎

Keywords: convexity , second order differentiability , Stepanov condition of order two , Takagi class , Taylor expansion of order two

Rights: Copyright © 2022 Michigan State University Press

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Vol.47 • No. 1 • 2022
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