Abstract
The so-called generalized associativity functional equation
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
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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Marichal, JL., Teheux, B. On the generalized associativity equation. Aequat. Math. 91, 265–277 (2017). https://doi.org/10.1007/s00010-016-0450-y
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DOI: https://doi.org/10.1007/s00010-016-0450-y