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ISSN : 1226-0657

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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: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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 <TEX>$$f(x+y)=e(x,y)g(x)h(y)$$</TEX>. From this result, we have the superstability of the exponential functional equation <TEX>$$f(x+y)=f(x)f(y)$$</TEX>.

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

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