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arXiv · 1907.09622

A note on Levi-Civita functional equation

Belfakih Keltouma·Elqorachi Elhoucien
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Abstract

In this paper we find the solutions of the functional equation $$f(xy) = g(x)h(y) + \sum_{j=1}^n g_j(x)h_j(y), \;x,y \in M,$$ where $M$ is a monoid, $n\geq 2$, and $g_j$ (for $j=1,...,n$) are linear combinations of at least $2$ distinct nonzero multiplicative functions.

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Belfakih Keltouma, Elqorachi Elhoucien. 2019-07-22. A note on Levi-Civita functional equation. https://arxiv.org/abs/1907.09622

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