Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x composite function y) = H(f(x), f(y)) (x, y in S) is investigated, where H is a homogeneous function and composite function is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.