Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces - Abasalt Bodaghi; Sang Og Kim (Abstract and Applied Analysis)
We obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when m is an even positive integer or m=3.