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Let $X$ be a vector space over a field $K$ of real or complex numbers and $ k\in \mathbb{N}$. We prove the superstability of the following generalized Golab--Schinzel type equation \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.
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참고문헌 (34)
참고문헌 신청
J. Aczel / 1970 / Remarks on one-parameter subsemigroups of the affine group and their homo- and isomorphisms / Aequationes Math 4:1~10
J. A. Baker / 1980 / The stability of the cosine equation / Proc. Amer. Math. Soc 80(3):411~416
J. A. Baker / 1979 / The stability of the equation f(x + y) =f(x)f(y) / Proc. Amer. Math. Soc 74(2):242~246
K. Baron / 1989 / On the continuous solutions of the Golab–Schinzel equation / Aequationes Math 38(2-3):155~162
N. Brillouet-Belluot / 1991 / On some functional equations of Golab–Schinzel type / Aequationes Math 42(2-3):239~270
J. A. Baker / 1980 / The stability of the cosine equation / Proc. Amer. Math. Soc 80(3):411~416
J. A. Baker / 1979 / The stability of the equation f(x + y) =f(x)f(y) / Proc. Amer. Math. Soc 74(2):242~246
K. Baron / 1989 / On the continuous solutions of the Golab–Schinzel equation / Aequationes Math 38(2-3):155~162
N. Brillouet-Belluot / 1991 / On some functional equations of Golab–Schinzel type / Aequationes Math 42(2-3):239~270
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