SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

Lee, Young-Whan; Lee, Young-Whan; Kim, Gwang-Hui; Kim, Gwang-Hui; Lee, Jae-Ha; Lee, Jae-Ha

P-ISSN3059-0604
E-ISSN3059-1309
KCI

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Vol.15 No.2

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SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

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

2008, v.15 no.2, pp.169-178

Lee, Young-Whan
Kim, Gwang-Hui
Lee, Jae-Ha

Lee,, Y. , Kim,, G. , & Lee,, J. (2008). SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION. , 15(2), 169-178.

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Abstract

In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation <TEX> $f(x+y)\;=\;a^{xy}f(x)f(y)$ </TEX> and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting <TEX> $|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$ </TEX>

keywords: exponential functional equation, stability of functional equation, superstability, solution of functional equation

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Article Contents

Vol.15 No.2

SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics