Cauchy type functional equations related to some associative rational functions

Katarzyna Domańska

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.


Full Text: PDF

Download statistics: 764

Licencja Creative Commons
This article by Katarzyna Domańska is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej