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Arithmetic subderivatives and Leibniz-additive functions
University of Tampere, Finland.
University of Tampere, Finland.
Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.ORCID iD: 0000-0002-7494-4632
2019 (English)In: Annales Mathematicae et Informaticae, ISSN 1216-6014Article in journal (Refereed) Epub ahead of print
Abstract [en]

We introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. In order to generalize these notions a step further, we define that an arithmetic function 𝑓 is Leibniz-additive if there is a nonzero-valued and completely multiplicative function ℎ𝑓 satisfying 𝑓(𝑚𝑛) = 𝑓(𝑚)ℎ𝑓 (𝑛) + 𝑓(𝑛)ℎ𝑓 (𝑚) for all positive integers 𝑚 and 𝑛. We study some basic properties of such functions. For example, we present conditions when an arithmetic function is Leibniz-additive and, generalizing the well-known bounds for the arithmetic derivative, we establish bounds for a Leibniz-additive function.

Place, publisher, year, edition, pages
Hungary: Eszterházy Károly College , 2019.
Keywords [en]
arithmetic derivative, Leibniz rule, additivity, multiplicativity
National Category
Mathematics Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-76244DOI: 10.33039/ami.2019.03.003OAI: oai:DiVA.org:ltu-76244DiVA, id: diva2:1357894
Available from: 2019-10-04 Created: 2019-10-04 Last updated: 2019-10-07

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Tossavainen, Timo

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2021222324252623 of 92
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