Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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APPROXIMATE GENERALIZED EXPONENTIAL FUNCTIONS

  • Received : 2009.07.28
  • Accepted : 2009.09.15
  • Published : 2009.09.25
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Abstract

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

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References

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