Orthogonal stability of an additive-quartic functional equation with the fixed point alternative

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation f (2x + y) + f (2x - y) = 4f (x + y) + 4f (x - y) + 10f (x) + 14f (-x) - 3f(y) - 3f (-y) for all x, y with x perpendicular to y, where perpendicular to is the orthogonality in the sense of Ratz.