On the stability of generalized gamma functional equation

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.