On Stability of a Functional Equation Connected with the Reynolds Operator

Let (X, ￠ ) be an Abelain semigroup, g:X ￠ ’X, and let K be either ￠ or ￠ . We prove superstability of the functional equation f(x ￠ g(y))=f(x)f(y) in the class of functions f:X ￠ ’K. We also show some stability results of the equation in the class of functions f:X ￠ ’Kn.