on the superstability and stability of the pexiderized exponential equation

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. furthermore, in connection with the open problem of th.m. rassias and our results we generalized the theorem of baker,lawrence, zorzitto and theorem of l. sz$acute{e}$kelyhidi.