The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS

  • Lee, Young-Whan (Department of Computer Hacking and Information Security, College of Natural Science, Daejeon University)
  • Received : 2012.04.05
  • Accepted : 2012.05.14
  • Published : 2012.05.31
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Abstract

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

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References

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