Lee, Eun-Hwi

  • Received : 2009.09.01
  • Published : 2010.12.25


We prove the superstability of a functional inequality associated with general exponential functions as follows; ${\mid}f(x+y)-a^{x^2y+xy^2}g(x)f(y){\mid}{\leq}H_p(x,y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker.


Exponential functional equation;Stability of functional equation;Superstability


  1. J. Baker, The stability of the cosine equations, Proc. Amer. Math. Soc. 80 (1980), 411-416.
  2. J. Baker, J. Lawrence And F. Zorzitto, The stability of the equations, f(x+y)=f(y), Proc. Amer. Math. Soc. 74 (1979), 242-246.
  3. G. L. Forti, Hyers-Ulam stability of functional equations, in several variables, Aequationes Math. 50 (1995), 146-190.
  4. R. Ger, Superstability is not natural, Rocznik Naukowo-Dydaktyczny WSP Krakkowie, Prace Mat. 159 (1993), 109-123.
  5. D.H. Hyers, On the stabliity of the linear functional equations, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224.
  6. D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequatioues Math. 44 (1992), 125-153.
  7. D.H. Hyers, G. Isac, and Th.M. Rassias, Stability of Stability of functional equations in Seeral variabler, Birkhauser-Basel-Berlin(1998).
  8. K.W. Jun, G,H. Kim and Y.W. Lee, Stability of generalized gamma and beta functional equations, Aequation Math. 60(2000), 15-24.
  9. S.-M. Jung, On the gerneral Hyers-Ulam stability of gamma functional equation, Bull. Korean Marth. Sec. 34. No 3 (1997), 437-446.
  10. S.-M. Juug. On the stability of the gammer functional equations, Results Math. 33 (1998), 306-309.
  11. G.H. Kim, and Y.W. Lee, The stability of the beta functional equation, Babes-Bolyai Mathematica, XLA (1)(2000), 89-96.
  12. Y.W. Lee, On the stability of a quadratic Jensen type functional equations, J. Math. Anal. Appl. 270 (2002) 590-601.
  13. Y.W. Lee, The stability of derivations on Banach algebras, Bull. Institute of Math. Academia Sinica, 28 (2000), 113-116.
  14. Y.W. Lee and B..M. Choi, The stability of Cauchy's gamma-beta functional equation, J. Math. Anal. Appl. 299 (2004), 305-313.
  15. Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  16. Th.M. Rassias, On a problem of S. M. Ulam and the asymptotic stabilityl of the Cauchy functional equation with applications, General Inequalities 7. MFO. Oberwolfach. Birkhauser Verlag. Basel ISNM Vol 123 (1997), 297-309.
  17. Th.M. Rassias, On the stability of the quadratic functional equation and its applications, Studia. Univ. Babes-Bolyai XLIII (3). (1998), 89-124.
  18. Th.M. Rassias, The problem of S. M. Ulam for approximately multiplication mappings, J. Math. Anal. Appl. 246 (2000), 352-378.
  19. Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284.
  20. Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Applications. Math. 62 (2000), 23-130.
  21. Th.M. Rassias and P. Semrl, On the behavior of mapping that do not stability Hyers-Ulam stability, Proc. Amer. Math. soc. 114 (1992), 989-993.
  22. S.M. Ulam, Problems in Modern Mathematics, Proc. Chap. VI. Wiley. NewYork, 1964.

Cited by

  1. Hyperstability and Superstability vol.2013, 2013,