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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.
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참고문헌 (13)
참고문헌 신청
D.G. Bourgin / 1949 / Approximately isometric and multiplicative transformations on continuous function rings / Duke Math. J 16 : 385 ~ 397
D.H. Hyers / 1941 / On the stability of the linear functional equation / Proc. Nat. Acad. Sci. USA 27 : 222 ~ 224
G. Kim / 2011 / Stability of the Lobacevski equation / J. Nonlinear Sci. Appl 4 : 11 ~ 18
G. Kim / 2011 / Stability of the Pexiderized Lobacevski equation / J. Appl. Math 2011
G.L. Forti / 1995 / Hyers-Ulam stability of functional equations in several variables / Aequationes Math 50 : 143 ~ 190
D.H. Hyers / 1941 / On the stability of the linear functional equation / Proc. Nat. Acad. Sci. USA 27 : 222 ~ 224
G. Kim / 2011 / Stability of the Lobacevski equation / J. Nonlinear Sci. Appl 4 : 11 ~ 18
G. Kim / 2011 / Stability of the Pexiderized Lobacevski equation / J. Appl. Math 2011
G.L. Forti / 1995 / Hyers-Ulam stability of functional equations in several variables / Aequationes Math 50 : 143 ~ 190
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