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On a Quantitative Theory of Limits: Estimating the Speed of Convergence

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Abstract

The classical “ε-δ” definition of limits is of little use to quantitative purposes, as is needed, for instance, for computational and applied mathematics. Things change whenever a realistic and computable estimate of the function δ(ε) is available. This may be the case for Lipschitz continuous and Hölder continuous functions, or more generally for functions admitting of a modulus of continuity. This, provided that estimates for first derivatives, fractional derivatives, or the modulus of continuity might be obtained. Some examples are given.

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Authors and Affiliations

  1. Department of Mathematics and Physics, “Roma Tre” University, 1, Largo S.L. Murialdo–, 00146, Rome, Italy

    Renato Spigler

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  1. Renato Spigler
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Correspondence to Renato Spigler.

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Spigler, R. On a Quantitative Theory of Limits: Estimating the Speed of Convergence. Fract Calc Appl Anal 23, 1013–1024 (2020). https://doi.org/10.1515/fca-2020-0053

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  • DOI: https://doi.org/10.1515/fca-2020-0053

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