Cauchy type functional equations related to some associative rational functions
Keywords:
functional equation, rational function, associativityAbstract
L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.
References
Chéritat, Arnaud. "Fractions rationnelles associatives et corps quadratiques." Revue des Mathématiques de l’Enseignement Supérieur 109 (1998-1999): 1025-1040.
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Daróczy, Zoltán and László Losonczi. "Über die Erweiterung der auf einer Punktmenge additiven Funktionen." Publ. Math. Debrecen 14 (1967): 239-245.
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Domańska, Katarzyna. "An analytic description of the class of rational associative functions." Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012): 111-122.
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Losonczi, László. "Local solutions of functional equations." Glas. Mat. Ser. III 25(45), no. 1 (1990): 57-67.
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