대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제19권4호
  • /
  • Pages.701-713
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  • 2004
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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STABILITY OF A BETA-TYPE FUNCTIONAL EQUATION WITH A RESTRICTED DOMAIN

  • Lee, Young-Whan (Department of Computer and Information Security Daejeon University) ;
  • Choi, Byung-Mun (Department of Computer and Information Security Daejeon University)
  • 발행 : 2004.10.01
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초록

We obtain the Hyers-Ulam-Rassias stability of a betatype 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: $g(\varphi(x),\phi(y))-\psi(x,y)g(s,y)-\lambda(x,y)$\mid$\leq\varepsilon(x,y)$ and $\frac{g(\varphi(x),\phi(y))}{\psi(x,y),g(x,y)}-1 $\mid$ \leq\epsilon(x,y)$.

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참고문헌

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