- - - Research nstitute for natural sciences, Hanyang University Seoul ۰۴۷۶۳, Korea
- - - Department of Mathematics Hallym University Chuncheon ۲۴۲۵۲ Korea

In this paper, we solve the quadratic \alpha-functional equations ۲f(x) + ۲f(y) = f(x + y) + \alpha^{-۲}f(\alpha(x-y)); (۰.۱) where \alpha is a fixed non-Archimedean number with \alpha^{-۲}neq ۳. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic \alpha-functional equation (۰.۱) in non-Archimedean Banach spaces.

Hyers-Ulam stability, non-Archimedean normed space, direct method, Fixed point, quadratic alpha-functional equation