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Displaying similar documents to “On a new characterization of the exponential functions”

On Popoviciu-Ionescu Functional Equation

Jose M. Almira (2016)

Annales Mathematicae Silesianae

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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.