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GENERALIZED STABILITIES OF CAUCHY'S GAMMA-BETA FUNCTIONAL EQUATION

  • Lee, Eun-Hwi (Department of Game, Jeonju University) ;
  • Han, Soon-Yi (Department of Game, Jeonju University)
  • Received : 2008.07.30
  • Accepted : 2008.08.23
  • Published : 2008.09.25

Abstract

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

Keywords

Functional equation;Stability;Super stability;Cauchy functional equation;Gamma-beta functional equation

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