Reference : On the generalized associativity equation
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/28870
On the generalized associativity equation
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Teheux, Bruno mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Apr-2017
Aequationes Mathematicae
Springer
91
2
265-277
Yes (verified by ORBilu)
International
0001-9054
1420-8903
Basel
Switzerland
[en] Generalized associativity ; functional equation ; quasi-inverse
[en] 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.
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/28870
10.1007/s00010-016-0450-y
http://arxiv.org/abs/1607.08435

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