Cauchy type functional equations related to some associative rational functions
Abstract
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.
Keywords
functional equation; rational function; associativity
Mathematics Subject Classification (2010)
39B52
References
Chéritat, Arnaud. "Fractions rationnelles associatives et corps quadratiques." Revue des Mathématiques de l’Enseignement Supérieur 109 (1998-1999): 1025-1040.
Daróczy, Zoltán and László Losonczi. "Über die Erweiterung der auf einer Punktmenge additiven Funktionen." Publ. Math. Debrecen 14 (1967): 239-245.
Domańska, Katarzyna. "An analytic description of the class of rational associative functions." Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012): 111-122.
Losonczi, László. "Local solutions of functional equations." Glas. Mat. Ser. III 25(45), no. 1 (1990): 57-67.
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