Stability of a composite functional equation related to idempotent mappings (Q630498)

The author proves the Hyers-Ulam stability of the composite functional equation \[ f\left( f(x) - f(y)\right) = f(x+y) + f(x-y) -f(x)-f(y), \] which was introduced by \textit{W. Fechner} [Aequationes Math. 78, No.~1--2, 185--193 (2009; Zbl 1207.39026)]. Here \(f\) is a continuous mapping from a Banach space to itself.