GENERALIZED STABILITIES OF CAUCHY'S GAMMA-BETA FUNCTIONAL EQUATION

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 3,  2008, pp.567-579
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.3.567
Title & Authors
GENERALIZED STABILITIES OF CAUCHY'S GAMMA-BETA FUNCTIONAL EQUATION
Lee, Eun-Hwi; Han, Soon-Yi;

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: $\small{{\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 $\small{{\leq}}$ p < 1).
Keywords
Functional equation;Stability;Super stability;Cauchy functional equation;Gamma-beta functional equation;
Language
English
Cited by
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