A functional equation with a symmetric binary operation

Autor: Judita Dascăl, Zoltán Daróczy
Rok vydání: 2011
Předmět:
Zdroj: Aequationes mathematicae. 82:291-297
ISSN: 1420-8903
0001-9054
DOI: 10.1007/s00010-011-0095-9
Popis: Let X be a nonempty set containing at least two elements and let \({\circ :X^2\to X}\) be a symmetric binary operation. Furthermore, let A, B, C be real parameters and let \({f,g:X\to\mathbb{R}_+}\) be unknown functions. We investigate the functional equation $$f(x\circ y)[Ag(y)-Bg(x)]=(A+C)f(x)g(y)-(B+C)f(y)g(x)\quad {\rm for\,\,all}\,x,y \in X.$$
Databáze: OpenAIRE
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