Communications of the
Korean Mathematical Society CKMS

We obtain the Hyers-Ulam-Rassias stability of a beta-type functional equation $$f( \varphi (x), \phi (y))= \psi (x, y)f(x, y)+ \lambda (x, y)$$ with a restricted domain and the stability in the sense of R. Ger of the equation $$f( \varphi (x), \phi (y))= \psi (x, y)f(x, y)$$ with a restricted domain in the following settings: $$\mid g( \varphi (x), \phi(y)) - \psi(x, y)g(x, y)- \lambda (x, y) \mid \ \leq \epsilon (x, y)$$ and $$\mid \frac{ g( \varphi (x), \phi(y))}{ \psi(x, y), g(x, y)}-1 \mid \ \leq \epsilon(x, y). $$

Keywords: functional equation, stability of functional equation, Hyers-Ulam-Rassias stability

MSC numbers: 39B22, 39B72