### Quadratic $\alpha$-functional equations

Document Type : Research Paper

Authors

1 Research nstitute for natural sciences, Hanyang University Seoul 04763, Korea

2 Department of Mathematics Hallym University Chuncheon 24252 Korea

Abstract

In this paper, we solve the quadratic $\alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + \alpha^{-2}f(\alpha(x-y)); (0.1)$ where $\alpha$ is a fixed non-Archimedean number with $\alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $\alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

Keywords