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On a method of Pi-Calleja for describing additive generators of associative functions. (English) Zbl 0765.39005

The author reviews a method introduced by P. Pi-Calleja [\(2^\circ\) Sympos. Probl. Mat. Latino Améria, Villavicencio-Mendoza 21–25 Julio 1954, 199–280 (1954; Zbl 0058.33602)] for describing additive generators of some associative functions on closed intervals, i.e., given \(T\) such that \(T(x,T(y,z))=T(T(x,y),z)\) one looks for functions \(\varphi\) such that \(T(x,y)=\varphi(\varphi^{-1}(x)+\varphi^{-1}(y))\). Then the author proves a theorem extending the results of Pi-Calleja. The essence of this theorem is that assuming some rather weak conditions on \(T\) the existence of some additive generator \(\varphi\) is proved.

MSC:

39B22 Functional equations for real functions

Citations:

Zbl 0058.33602
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References:

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