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  • P-ISSN3059-0604
  • E-ISSN3059-1309
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ISSN : 3059-0604

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Vol.19 No.2

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APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.2, pp.193-198
https://doi.org/10.7468/jksmeb.2012.19.2.193
Lee, Young-Whan
Lee,, Y. (2012). APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS, 19(2), 193-198, https://doi.org/10.7468/jksmeb.2012.19.2.193

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 $$f(x+y)=f(x)f(y)$$.

keywords
functional equation, stability, superstability, gamma and beta functional equation, Cauchy functional equation, exponential functional equation

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