FUNCTIONAL EQUATIONS IN ORTHOGONALITY SPACES

Abstract

Using fixed point method, we prove the Hyers-Ulam
stability of the orthogonally additive functional equation
$f (2x + y) = 2f (x) + f (y)$
and of the orthogonally quadratic functional equation
$2f(\frac{x}{2}+y)+2f(\frac{x}{2}-y)=f(x)+4f(y)$

for all x, y with x ⊥ y in orthogonality spaces.