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.