On a direct method for proving the Hyers–Ulam stability of functional equations

We study the stability of an equation in a single variable of the form f ( x ) = a f ( h ( x ) ) + b f ( − h ( x ) ) with some conditions imposed on constants a, b and function h. The results are later applied for proving the stability (by use of a direct method) of a couple of functional equations in several variables. They let us not only shorten various approaches obtained during the last years but also improve the approximating constants.