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arXiv · 1607.08435

On the generalized associativity equation

Jean-Luc Marichal·Bruno Teheux
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Abstract

The so-called generalized associativity functional equation G(J(x,y),z) = H(x,K(y,z)) has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real, continuous, and strictly monotonic in each variable. In this note we investigate the following related problem: given the functions J and K, find every function F that can be written in the form F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) for some functions G and H. We show how this problem can be solved when any of the inner functions J and K has the same range as one of its sections.

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Jean-Luc Marichal, Bruno Teheux. 2016-07-28. On the generalized associativity equation. https://doi.org/10.1007/s00010-016-0450-y

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