On a quantitative theory of limits: Estimating the speed of convergence-Reference-Cited by-同舟云学术

On a quantitative theory of limits: Estimating the speed of convergence

Published:2020-08-01 Issue:4 Volume:23 Page:1013-1024
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Spigler Renato¹

Affiliation:

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0053/pdf

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