On Popoviciu-Ionescu functional equation

Jose M. Almira

Published: 2016-09-23

Vol. 30 (2016)

On Popoviciu-Ionescu functional equation

Jose M. Almira

Abstract

We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.

Keywords:

functional equations , exponential polynomials on Abelian groups , Montel type theorem

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Almira, J. M. (2016). On Popoviciu-Ionescu functional equation. Annales Mathematicae Silesianae, 30, 5–15. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13953

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Vol. 30 (2016)
Published: 2016-09-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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