On a direct method for proving the Hyers-Ulam stability of functional equations (Q2637935)

The author uses the direct method to investigate the stability of the functional equation \[ f(x)=\alpha f(h(x))+\beta f(-h(x)), \] where \(f : X \to Y\) is a function from a nonempty set \(X\) with an involution into a Banach space \((Y ,\|.\|)\) under certain conditions on the real constants \(\alpha, \beta\) and the odd function \(h: X \to X\). She then nicely applies her results for obtaining several various stability results.