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A functional equation and its application to the characterization of gamma distributions

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Abstract

The functional equation

$$ f\left(x\right)g\left(y\right)=p\left(x+y\right)q\left(\frac{x}{y} \right) $$

is investigated for almost all \({\left(x,\,y\right)\in\mathbb{R}^{2}_{+}}\) and for the measurable functions \({f,\,g,\,p,\,q:\mathbb{R}_{+}\rightarrow\mathbb{R}_{+}}\). This equation is related to the Lukács characterization of gamma distribution.

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References

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    Fruzsina Mészáros

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  1. Fruzsina Mészáros
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Correspondence to Fruzsina Mészáros.

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Dedicated to the 70th birthday of Professor Zoltán Daróczy

This research has been supported by the Hungarian Scientific Research Fund (OTKA), Grant NK 68040.

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Mészáros, F. A functional equation and its application to the characterization of gamma distributions. Aequat. Math. 79, 53–59 (2010). https://doi.org/10.1007/s00010-010-0008-3

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  • DOI: https://doi.org/10.1007/s00010-010-0008-3

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