On the generalized associativity equation
Rings and Algebras
2017-03-28 v1
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.
Keywords
Cite
@article{arxiv.1607.08435,
title = {On the generalized associativity equation},
author = {Jean-Luc Marichal and Bruno Teheux},
journal= {arXiv preprint arXiv:1607.08435},
year = {2017}
}