A fixed point approach to orthogonal stability of an additive-quadratic functional equation

Abstract

Using the fixed point method, we prove the Hyers-Ulam stabilityof the following orthogonally additive-quadratic functional equation

f(x+ay) =f(x) +a^{2}f(y)- (a^{2}- a)^{2}(f(x+y)- f(x- y))

where a \in N-{0,1}  in orthogonality spaces.