Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOLUTION AND STABILITY OF A GENERAL QUADRATIC FUNCTIONAL EQUATION IN TWO VARIABLES

  • LEE, EUN HWI (School of Natural Science, Jeonju University) ;
  • LEE, JO SEUNG (School of Natural Science, Jeonju University)
  • Received : 2003.10.15
  • Accepted : 2003.12.04
  • Published : 2004.03.25
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Abstract

In this paper we obtain the general solution the functional equation $a^2f(\frac{x-2y}{a})+f(x)+2f(y)=2a^2f(\frac{x-y}{a})+f(2y).$ The type of the solution of this equation is Q(x)+A(x)+C, where Q(x), A(x) and C are quadratic, additive and constant, respectively. Also we prove the stability of this equation in the spirit of Hyers, Ulam, Rassias and $G\check{a}vruta$.

Keywords

References

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