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ISSN : 1226-0657

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Vol.15 No.2

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SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.2, pp.169-178
Lee, Young-Whan (DEPARTMENT OF COMPUTER AND INFORMATION SECURITY, DAEJEON UNIVERSITY)
Kim, Gwang-Hui (DEPARTMENT OF MATHEMATICS, KANGNAM UNIVERSITY)
Lee, Jae-Ha (JUNG IL HIGH SCHOOL)
Lee, Young-Whan, Kim, Gwang-Hui, & Lee, Jae-Ha. (2008). SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION. 한국수학교육학회지시리즈B:순수및응용수학, 15(2), 169-178.

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

한국수학교육학회지시리즈B:순수및응용수학

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