Superstability of the generalized Pexider type exponential equation in Abelian group
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In this paper, we will prove the superstability of the following generalized Pexider type exponential equation \begin{eqnarray*}f\big(x+y\big)^m &=& g(x)h(y),\end{eqnarray*}where $f, g, h: G \to \mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here $G$ is an Abelian group $(G,+)$, and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G{\v a}vruta's result in 1994 and G. H. Kim's results in 2011.
Abstract
In this paper, we will prove the superstability of the following generalized Pexider type exponential equation \begin{eqnarray*}f\big(x+y\big)^m &=& g(x)h(y),\end{eqnarray*}where $f, g, h: G \to \mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here $G$ is an Abelian group $(G,+)$, and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G{\v a}vruta's result in 1994 and G. H. Kim's results in 2011.
참고문헌 (13)
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