Abstract
We deal with a conditional functional inequality x⊥y⇒‖f(x+y)−f(x)−f(y)‖≤ε(‖x‖p+‖y‖p), where ⊥ is a given orthogonality relation, ε is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition x⊥y⇒g(x+y)=g(x)+g(y). In the sequel, we deal with some other functional inequalities and we also present some applications and generalizations of the first result.