Two functional equations on groups



Abstract

In this note we give the general solution of the functional equation
f(x) f(x+y) = f(y)2 f(xy)2 g(y),  x,yG,
and all the solutions of
f(x) f(x+y) = f(y)2 f(xy)2 g(x) ,  x,yG,
with the additional supposition g(x) ≠ 0 for all xG. In both cases G denotes an arbitrary group written additively and f,g: G→ℝ are the unknown functions.


Keywords

functional equations; group; general solution

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Published : 2007-09-28


ÁdámZ., LajkóK., MaksaG., & MészárosF. (2007). Two functional equations on groups. Annales Mathematicae Silesianae, 21, 7-13. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14055

Zsolt Ádám 
Institute of Mathematics, University of Debrecen, Hungary  Hungary
Károly Lajkó 
Institute of Mathematics, University of Debrecen, Hungary  Hungary
Gyula Maksa 
Institute of Mathematics, University of Debrecen, Hungary  Hungary
Fruzsina Mészáros  mefru@math.klte.hu
Institute of Mathematics, University of Debrecen, Hungary  Hungary



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