Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

THE STABILITY OF A GENERALIZED CAUCHY FUNCTIONAL EQUATION

  • LEE, EUN HWI (Dept. of Mathematics, Jeonju University) ;
  • CHOI, YOUNG HO (Dept. of Mathematics Education, Jeonju University) ;
  • NA, YOUNG YOON (Dept. of Mathematics Education, Jeonju University)
  • Received : 2000.04.28
  • Published : 2000.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

We prove the stability of a generalized Cauchy functional equation of the form ; $$f(a_1x+a_2y)=b_1f(x)+b_2f(y)+w.$$ That is, we obtain a partial answer for the open problem which was posed by the Th.M Rassias and J. Tabor on the stability for a generalized functional equation.

Keywords

References

  1. J. Math. Anal. Appl. v.184 A generalization of the Hyers-Ulam-Rassias stability of approximate additive mappings Gavruta, P.
  2. Proc. Nat. Acad. Sci. On the stability of the linear functional equation Hyers, D.H.
  3. Proc. Amer. Math. Soc. v.72 On the stability of the linear functional equation Rassias, Th. M.
  4. J. Nat. Geometry v.1 What is left of Hyers-Ulam stability? Rassias, Th. M.;Tabor, J.
  5. Problems in Modern Mathematics, Chap. VI, Science editions Ulam, S.M.