International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 513-520
doi:10.1155/S0161171200003598
On the stability of generalized gamma functional equation
Department of Mathematics, Kangnam University, Suwon 449–702, Korea
Received 1 July 1999
Copyright © 2000 Gwang Hui Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We obtain the Hyers-Ulam stability and modified Hyers-Ulam
stability for the equations of the form g(x+p)=φ(x)g(x) in the following settings:
|g(x+p)−φ(x)g(x)|≤δ, |g(x+p)−φ(x)g(x)|≤ϕ(x), |(g(x+p)/φ(x)g(x))−1|≤ψ(x). As a consequence we obtain the stability theorems for the gamma
functional equation.