GENERAL STABILITY OF THE EXPONENTIAL AND LOBACEVSKII FUNCTIONAL EQUATIONS

Let S be a semigroup possibly with no identity and f : S -> C. We consider the general superstability of the exponential functional equation with a perturbation psi of mixed variables f(x + y) - f(x)f(y)vertical bar <= psi(x, y) for all x, y is an element of S. In particular, if S is a uniquely 2-divisible semigroup with an identity, we obtain the general superstability of Lobacevskii's functional equation with perturbation psi f(x + y/2)(2) - f(x)f(y)vertical bar <= psi(x, y) for all x, y is an element of S.