On Popoviciu-Ionescu Functional Equation

Author:

Almira Jose M.1

Affiliation:

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference26 articles.

1. [1] Aksoy A., Almira J.M., On Montel and Montel–Popoviciu theorems in several variables, Aequationes Math. 89 (2015), 1335–1357.

2. [2] Almira J.M., Montel’s theorem and subspaces of distributions which are Δm-invariant, Numer. Funct. Anal. Optim. 35 (2014), no. 4, 389–403.

3. [3] Almira J.M., Abu-Helaiel K.F., On Montel’s theorem in several variables, Carpathian J. Math. 31 (2015), 1–10.

4. [4] Almira J.M., Székelyhidi L., Montel-type theorems for exponential polynomials, Demonstratio Math. 49 (2016), no. 2, 197–212.

5. [5] Anselone P.M., Korevaar J., Translation invariant subspaces of finite dimension, Proc. Amer. Math. Soc. 15 (1964), 747–752.

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