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2018 | OriginalPaper | Buchkapitel

On Copson’s Theorem and Its Generalizations

verfasst von : A. Linero Bas, D. Nieves Roldán

Erschienen in: Differential and Difference Equations with Applications

Verlag: Springer International Publishing

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Abstract

E.T. Copson generalized the well-known result about the convergence of bounded and monotonic sequences of real numbers. Over the years, generalizations of this result have been made concerning linear and nonlinear inequalities that gave us a wide range of criteria for the convergence of sequences in relationship to the characteristic polynomial, monotonicity of the variables, etc. In this paper, we present a survey about these generalizations of Copson’s result, focusing in the state-of-art of the problem, and bring up some open questions that could lead us to future research.

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Metadaten
Titel
On Copson’s Theorem and Its Generalizations
verfasst von
A. Linero Bas
D. Nieves Roldán
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-75647-9_28