On the Superstability and Stability of the Pexiderized Exponential Equation

Document Type: Research articles


Department of Mathematics, University of Mazandaran


The main purpose of this paper is to establish some new results on
the superstability and stability via a fixed point approach for
the 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 arbitrary
commutative semigroup $S$ to an arbitrary unitary complex Banach
algebra and also $\psi: S^{2}\rightarrow [0,\infty)$ is a
function. 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.