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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The stability of certain functional equations


Author: John A. Baker
Journal: Proc. Amer. Math. Soc. 112 (1991), 729-732
MSC: Primary 39B52
MathSciNet review: 1052568
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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.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1052568-7
PII: S 0002-9939(1991)1052568-7
Keywords: Functional equations, stability, fixed points
Article copyright: © Copyright 1991 American Mathematical Society