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Fixed points, stability, and harmless perturbations

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Much has been written about systems in which each constant is a solution and each solution approaches a constant. It is a small step to conjecture that functions promoting such behavior constitute harmless perturbations of stable equations. That idea leads to a new way of avoiding delay terms in a functional-differential equation. In this paper we use fixed point theory to show that such a conjecture is valid for a set of classical equations.

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Correspondence to TA Burton.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Burton, T. Fixed points, stability, and harmless perturbations. Fixed Point Theory Appl 2005, 364505 (2005). https://doi.org/10.1155/FPTA.2005.35

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  • DOI: https://doi.org/10.1155/FPTA.2005.35