Generalized orthogonal stability of some functional equations

We deal with a conditional functional inequality , where is a given orthogonality relation, is a given nonnegative number, and is a given real number. Under suitable assumptions, we prove that any solution of the above inequality has to be uniformly close to an orthogonally additive mapping , that is, satisfying the condition . In the sequel, we deal with some other functional inequalities and we also present some applications and generalizations of the first result.