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Annales Mathematicae Silesianae

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On Popoviciu-Ionescu Functional Equation

Jose M. Almira
  • Departamento de Matemáticas, Universidad de Jaén, E.P.S. Linares, Campus Científico Tecnológico de Linares, Cinturón Sur s/n, 23700 Linares, Spain
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Published Online: 2016-09-23 | DOI: https://doi.org/10.1515/amsil-2016-0006


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

MSC 2010: 39B22; 39A70; 39B52


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About the article

Received: 2016-03-31

Revised: 2016-05-14

Accepted: 2016-05-19

Published Online: 2016-09-23

Published in Print: 2016-09-01

Citation Information: Annales Mathematicae Silesianae, Volume 30, Issue 1, Pages 5–15, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2016-0006.

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© 2016 Jose M. Almira, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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