ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation f(x/2 + y) + f(x/2 - y) + f(x/2 + z) + f(x/2 - z) (0.1) = 3/2f(x) - 1/2f(-x) + f(y) + f(-y) + f(z) + f(-z) for all x, y, z with x perpendicular to y, in orthogonality Banach spaces and in non- Archimedean orthogonality Banach spaces.