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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Acknowledgements
This paper has been partially supported by the grant number MTM2014-52920_p from Ministerio de Economía y Competitividad (Spain). We also greatly appreciate the financial support to the second author given by Department of Mathematics, University of Murcia.
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Linero Bas, A., Nieves Roldán, D. (2018). On Copson’s Theorem and Its Generalizations. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_28
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DOI: https://doi.org/10.1007/978-3-319-75647-9_28
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