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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1052568-7
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: \[ f(t) = \alpha (t) + \beta (t)f(\phi (t)),\] where $\alpha$ and $\beta$ are given complex valued functions defined on a nonempty set $S$ such that $\sup \{ |\beta (t)|:t \in S\} < 1$ and $\phi$ is a given mapping of $S$ into itself.


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Keywords: Functional equations, stability, fixed points
Article copyright: © Copyright 1991 American Mathematical Society