Functional equations in orthogonality spaces

Abstract

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) f (2x + y) = 2f(x) + f(y)and of the orthogonally quadratic functional equation 2f (x 2+ y )+ 2f (x 2− y )(0.2) = f(x) + 4f(y)for all x; y with x ⊥ y in orthogonality spaces.