On the stability of the functional equation $\varphi [f(x)]=g(x)\varphi (x)+F(x)$
Author:
Dobiesław Brydak
Journal:
Proc. Amer. Math. Soc. 26 (1970), 455-460
MSC:
Primary 39.30
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265801-2
MathSciNet review:
0265801
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper gives results on the stability of the solutions of $\varphi [f(x)] = g(x)\varphi (x) + F(x)$ where $f,g$ and $F$ are given functions and $\varphi$ is unknown.
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224. MR 4076, DOI https://doi.org/10.1073/pnas.27.4.222
- D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288–292. MR 13219, DOI https://doi.org/10.1090/S0002-9904-1945-08337-2
- D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous functions, Ann. of Math. (2) 48 (1947), 285–289. MR 20717, DOI https://doi.org/10.2307/1969171
- Marek Kuczma, Functional equations in a single variable, Monografie Matematyczne, Tom 46, Państwowe Wydawnictwo Naukowe, Warsaw, 1968. MR 0228862
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Keywords:
Functional equation,
stability
Article copyright:
© Copyright 1970
American Mathematical Society