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.
@article{bwmeta1.element.doi-10_1515_amsil-2016-0006,
author = {Jose M. Almira},
title = {On Popoviciu-Ionescu Functional Equation},
journal = {Annales Mathematicae Silesianae},
volume = {30},
year = {2016},
pages = {5-15},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0006}
}
Jose M. Almira. On Popoviciu-Ionescu Functional Equation. Annales Mathematicae Silesianae, Tome 30 (2016) pp. 5-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0006/