Quadratic \alpha-functional equations

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.

Keywords:

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