University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)1735-06111220120701On the Superstability and Stability of the Pexiderized Exponential Equation617445ENMohsen AlimohammadyDepartment of Mathematics, University of MazandaranAli SadeghiDepartment of Mathematics, University of MazandaranJournal Article20111101The main purpose of this paper is to establish some new results on<br />the superstability and stability via a fixed point approach for<br />the Pexiderized exponential equation, i.e.,<br />$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$<br />where $f$, $g$ and $h$ are three functions from an arbitrary<br />commutative semigroup $S$ to an arbitrary unitary complex Banach<br />algebra and also $psi: S^{2}rightarrow [0,infty)$ is a<br />function. Furthermore, in connection with the open problem of Th.<br />M. Rassias and our results we generalized the theorem of Baker,<br />Lawrence, Zorzitto and theorem of L. Sz$acute{e}$kelyhidi.http://cjms.journals.umz.ac.ir/article_45_f7d32d951e0682ec78c76d90b94637e6.pdf