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Second and third order forward difference operator: what is in between?

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, we present a new geometrical notion for a real-valued function defined in a discrete domain that depends on a parameter \(\alpha \ge 2.\) We give examples to illustrate connections between convexity and this new concept. We then prove two criteria based on the sign of the discrete fractional operator of a function u,  \(\Delta ^{\alpha }u\) with \(2 \le \alpha < 4.\) Two examples show that the given criteria are optimal with respect to the established geometrical notion.

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Funding

J. Bravo is supported by ANID-PFCHA/Doctorado Nacional/2019-21190764. C. Lizama is partially supported by FONDECYT grant number 1180041. S. Rueda is supported by ANID-PFCHA/Doctorado Nacional/2017-21171405.

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Authors and Affiliations

  1. Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

    Jennifer Bravo, Carlos Lizama & Silvia Rueda

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  1. Jennifer Bravo
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  2. Carlos Lizama
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  3. Silvia Rueda
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Correspondence to Carlos Lizama.

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Bravo, J., Lizama, C. & Rueda, S. Second and third order forward difference operator: what is in between?. RACSAM 115, 86 (2021). https://doi.org/10.1007/s13398-021-01015-5

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