Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ON STABILITY OF THE EQUATION - g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$

  • Published : 2000.09.01

⟨ Previous Next ⟩

Abstract

On the positive real number, we obtain the Hyers-Ulam stability and a stability in the sense of R. Ger for the generalized beta function g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$ in the following settings: $$\mid$g(x+p,y+q)-{\varphi}(x,y)g(x,y)$\mid${\leq}{\delta}$ and $$\mid$\frac{g(x+p,y+q)}{\varphi(x,y)g(x,y)}-1$\mid${\leq}{\psi}(x,y). As a consequence we obtain stability theorems for the gamma functional equation and the beta functional equation.

Keywords

References

  1. Proc. Amer. Math. Soc. v.74 The stability of the equation f(x + u) = f(x) + f(y) J. Baker;J. Lawrence;F. Zorzitto
  2. Aequatioues Math. v.54 On Hyers-Ulam stability for a class of functional equations C. Borelli
  3. Aequatioues Math. v.50 Hyers-Ulam stability of functional equations in several variables G. L. Forti
  4. Naukowo-Kydaktyczny WSP w. Krakowie, Prace Mat. v.159 Superstability is not natural R. Ger
  5. Proc. Nat. acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D. H. Hyers
  6. Aequatioues Math. v.44 Approximate homomorphisms D. H. Hyers;T. M. Rassias
  7. Bull. Korean Math. Soc. v.34 no.3 On the general Hyers-Ulam stability of gamma functional equation S. M. Jung
  8. Results Math. v.33 On the stability of the gamma functional equation S. M. Jung
  9. The stability of the Beta functional equation G. H. Kim;Y. W. Lee
  10. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces T. M. Rassias
  11. Problems in Modern Mathematics, Chap.Ⅵ(Science editions) S. M. Ulam