STABILITY OF THE G-FUNCTIONAL EQUATION

  • Published : 2002.05.01

Abstract

In this paper, we obtain the Hyers-Ulam Stability for the difference equations of the form f(x + 1) = $\Gamma$(x)f(x), which is the reciprocal functional equation of the double gamma function.

Keywords

References

  1. Result. math. v.35 Remark on the stability of the Gamma functional equation H.Alzer
  2. Quart. J. Math. v.31 The theory of the G-function E.W.Barnes
  3. Proc. London Math. Soc. v.31 Genesis of the double gamma function E.W.Barnes
  4. Proc. Roy. Soc. London Ser. A v.196 The theory of the double gamma function E.W.Barnes
  5. J. Math. Anal. Appl. v.231 Certain classes of series involving the Zeta function J.Choi;H.M.Srevastava
  6. Bull. Austral. Math. Soc. v.51 Some series involving the Zeta function J. Choi;H.M.Srivastava;J.R.Quine
  7. Roczik Naukowo-Dydaktyczny WSP w Krakowie, Prace Mat. v.159 Superstability is not natural R.Ger
  8. Proc. Nat. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H.Hyers
  9. Stability of functional equation in Several Variables D.H.Hyers;G.Isac;Th.M.Rassias
  10. Aequations Math. v.60 Stability of generalized gamma and beta functional equations K.W.Jun;G.H.Kim;Y.W.Lee
  11. Results Math. v.33 On the stability of gamma functional equation S.M.Jung
  12. Internat. J. Math. & Math. Sci. v.23 On the stability of generalized gamma functional equation G.H.Kim
  13. Math. Proc. Cambridge Philos. Soc. v.123 Asympototic series for double zeta, double gamma and Hecke L-functions Matsumoto
  14. J. Funct. Anal. v.80 Extremals of determinants of Laplacians B.Osgood;R.Philips;P.Sarnak
  15. Proc. Amer. Math. Soc. v.114 On the behavior of mappings which do not satisfy Hyers-Ulam stability Th.M.Rassias;P.Semrl
  16. Tokyo J. Math. v.1980 A proof of the classical Kronecker limit formula T.Shintani
  17. Problems in Modern Mathematics(Science eds.) S.M.Ulam
  18. SIAM J. Math. Anal. v.19 Determinants of Laplacians and multiple gamma functions I.Vardi
  19. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th.M.Rassias