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The stability of certain functional equations


Author: John A. Baker
Journal: Proc. Amer. Math. Soc. 112 (1991), 729-732
MSC: Primary 39B52
DOI: https://doi.org/10.1090/S0002-9939-1991-1052568-7
MathSciNet review: 1052568
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Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to prove the stability (in the sense of Ulam) of the functional equation:

$\displaystyle f(t) = \alpha (t) + \beta (t)f(\phi (t)),$

where $ \alpha $ and $ \beta $ are given complex valued functions defined on a nonempty set $ S$ such that $ \sup \{ \vert\beta (t)\vert:t \in S\} < 1$ and $ \phi $ is a given mapping of $ S$ into itself.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1052568-7
Keywords: Functional equations, stability, fixed points
Article copyright: © Copyright 1991 American Mathematical Society

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