The main results of the paper concern functional equations of the form f(M(x,y))(g(y) - g(x)) = μ(f(x)g(y) - f(y)g(x)) (x, y ∈ I), where f and g are continuous functions defined on an open interval I and M is a strict two variable mean on I. As an application, a generalization of the so-called Matkowski-Sutô problem for weighted two variable quasi-arithmetic means is solved under first-order continuous differentiability assumptions.
|Number of pages||15|
|Publication status||Published - Jan 1 2003|
- Functional equation
- Matkowski-Sutô problem
- Stolarsky means
- Weighted quasi-arithmetic mean
ASJC Scopus subject areas