论文信息 - On the stability of generalized gamma functional equation

On the stability of generalized gamma functional equation

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.

Gwang Hui Kim | G. Kim

[1] Roman Ger,et al. The stability of the exponential equation , 1996 .

[2] S. Ulam. Problems in modern mathematics , 1964 .

[3] On the Stability of Gamma Functional Equation , 1998 .

[4] Soon-Mo Jung,et al. On a general hyers-ulam stability of gamma functional equation , 1997 .

[5] D. H. Hyers. On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[6] P. Gǎvruţa,et al. A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings , 1994 .

[7] Changgui Zhang. Sur la fonction q-Gamma de Jackson , 2001 .

[8] T. Rassias. On the stability of the linear mapping in Banach spaces , 1978 .

[9] V. Kac,et al. q-Gamma and q-Beta Functions , 2002 .

[10] Z. Páles,et al. Generalized stability of the Cauchy functional equation , 1998 .

[11] R D Luce,et al. Hyers-ulam stability of functional equations with a square-symmetric operation. , 1998, Proceedings of the National Academy of Sciences of the United States of America.