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.
Park, C. & Kim, S. O. (2017). Quadratic $\alpha$-functional equations. International Journal of Nonlinear Analysis and Applications, 8(1), 1–9. https://doi.org/10.22075/ijnaa.2017.1066.1218
MLA
Park, C., & Kim, S. O. "Quadratic $\alpha$-functional equations", International Journal of Nonlinear Analysis and Applications, 8, 1, 2017, 1–9. doi: 10.22075/ijnaa.2017.1066.1218
HARVARD
Park, C., & Kim, S. O. (2017). 'Quadratic $\alpha$-functional equations', International Journal of Nonlinear Analysis and Applications, 8(1), pp. 1–9. doi: 10.22075/ijnaa.2017.1066.1218
CHICAGO
Park, C. & Kim, S. O., "Quadratic $\alpha$-functional equations." International Journal of Nonlinear Analysis and Applications, 8 1 (2017): 1–9, doi: 10.22075/ijnaa.2017.1066.1218
VANCOUVER
Park C., Kim S. O. Quadratic $\alpha$-functional equations. IJNAA. 2017;8(1):1–9. doi: 10.22075/ijnaa.2017.1066.1218
International Journal of Nonlinear Analysis and Applications