On Popoviciu-Ionescu Functional Equation

Jose M. Almira

doi:10.1515/amsil-2016-0006

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On Popoviciu-Ionescu Functional Equation

Annales Mathematicae Silesianae

Volume 30 (2016): Issue 1 (September 2016)

By: Jose M. Almira

Open Access

|Sep 2016

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.

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Articles in this issue

DOI: https://doi.org/10.1515/amsil-2016-0006 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 5 - 15

Submitted on: Mar 31, 2016

Accepted on: May 19, 2016

Published on: Sep 23, 2016

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

functional equations,

exponential polynomials on Abelian groups,

Montel type theorem

Related subjects:

Mathematics,

General mathematics

© 2016 Jose M. Almira, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2016): Issue 1 (September 2016)