The stability of certain functional equations

Baker, John A.

doi:10.1090/S0002-9939-1991-1052568-7

The stability of certain functional equations
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by John A. Baker

Proc. Amer. Math. Soc. 112 (1991), 729-732

DOI: https://doi.org/10.1090/S0002-9939-1991-1052568-7

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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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