<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We study a functional equation first proposed by T. Popoviciu <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_015_w2aab2b8c22b1b7b1ab1ac15Aa">[15]</xref> in 1955. It was solved for the easiest case by Ionescu <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_009_w2aab2b8c22b1b7b1ab1ab9Aa">[9]</xref> in 1956 and, for the general case, by Ghiorcoiasiu and Roscau <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_007_w2aab2b8c22b1b7b1ab1ab7Aa">[7]</xref> and Radó <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_017_w2aab2b8c22b1b7b1ab1ac17Aa">[17]</xref> 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.</p></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.

On Popoviciu-Ionescu Functional Equation

Departamento de Matemáticas, Universidad de Jaén, E.P.S. Linares, Campus Científico Tecnológico de Linares, Cinturón Sur s/n, 23700 Linares,

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On Popoviciu-Ionescu Functional Equation"}

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...

On Popoviciu-Ionescu Functional Equation

Published Online: Sep 23, 2016

Page range: 5 - 15

Received: Mar 31, 2016

Accepted: May 19, 2016

DOI: https://doi.org/10.1515/amsil-2016-0006

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

© 2016 Jose M. Almira, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Popoviciu-Ionescu Functional Equation

Published Online: Sep 23, 2016

Page range: 5 - 15

Received: Mar 31, 2016

Accepted: May 19, 2016

DOI: https://doi.org/10.1515/amsil-2016-0006

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

© 2016 Jose M. Almira, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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