Department of Mathematics, University of Mazandaran
Abstract
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.
Alimohammady, M. , & Sadeghi, A. (2012). On the Superstability and Stability of the Pexiderized Exponential Equation. Caspian Journal of Mathematical Sciences, 1(2), 61-74.
MLA
Mohsen Alimohammady; Ali Sadeghi. "On the Superstability and Stability of the Pexiderized Exponential Equation", Caspian Journal of Mathematical Sciences, 1, 2, 2012, 61-74.
HARVARD
Alimohammady, M., Sadeghi, A. (2012). 'On the Superstability and Stability of the Pexiderized Exponential Equation', Caspian Journal of Mathematical Sciences, 1(2), pp. 61-74.
CHICAGO
M. Alimohammady and A. Sadeghi, "On the Superstability and Stability of the Pexiderized Exponential Equation," Caspian Journal of Mathematical Sciences, 1 2 (2012): 61-74,
VANCOUVER
Alimohammady, M., Sadeghi, A. On the Superstability and Stability of the Pexiderized Exponential Equation. Caspian Journal of Mathematical Sciences, 2012; 1(2): 61-74.
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