Notes on Stability of the Generalized Gamma Functional Equation

for some positive constant ε depending only on δ. Sometimes we call f a δ-approximate solution of (1.1) and g ε-close to f . Such an idea of stability was given by Ulam [13] for Cauchy equation f(x+y) = f(x)+f(y) and his problem was solved by Hyers [4]. Later, the Hyers-Ulam stability was studied extensively (see, e.g., [6, 8, 10, 11]). Moreover, such a concept is also generalized in [2, 3, 12]. As in [5] we say (1.1) has the generalized Hyers-Ulam-Rassias stability if for an approximate solution f , such that ∣∣E1(f )(x)−E2(f )(x)∣∣≤ψ(x) (1.4)