Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SUPERSTABILITY OF A GENERALIZED EXPONENTIAL FUNCTIONAL EQUATION OF PEXIDER TYPE

  • Lee, Young-Whan (DEPARTMENT OF COMPUTER AND INFORMATION SECURITY DAEJEON UNIVERSITY)
  • Published : 2008.07.31
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Abstract

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

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