MMN-2239
Additive $(\alpha, \beta)$-functional equations and linear mappings
Choonkil Park;Abstract
In this paper, we investigate the additive $(\alpha,\beta)$-functional equation $$f(x)+\overline{\alpha}f(\alpha y)+ f(z)=\beta^{-1}f(\beta(x+y+z))$$
for all complex numbers $\alpha$ with $|\alpha|=1$ and for a fixed nonzero complex number $\beta$.
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the above additive $(\alpha,\beta)$-functional equation in complex Banach spaces.
Vol. 19 (2018), No. 2, pp. 1107-1115