Year: 2026
Type: article
Abstract: We investigate the functional equation $$f(f(x+y))=f(x+y)+f(x)f(y),\ x,y\in \mathbb R.$$ f ( f ( x + y ) ) = f ( x + y ) + f ( x ) f ( y ) , x , y ∈ R . Given a real number $$c\ne 0,$$ c ≠ 0 , it was shown in [5] that there is a non-trivial solution f with $$f(0)=c$$ f ( 0 ) = c iff c is transcendental and $$>-1$$ > - 1 . In that case all values of f are transcendental. In this paper we find all solutions of the functional equation, discuss their odd properties and the connection with ideals in a group algebra.
Source: Ricerche di Matematica
Author: Johannes Schoißengeier
Institution: University of Vienna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Universität Wien
OpenAlex ID: W7161175341