2021 Sequential derivatives
Steen Pedersen, Joseph P. Sjoberg
Author Affiliations +
Real Anal. Exchange 46(1): 191-206 (2021). DOI: 10.14321/realanalexch.46.1.0191

Abstract

Consider a real valued function defined, but not differentiable at some point. We use sequences approaching the point of interest to define and study sequential concepts of secant and cord derivatives of the function at the point of interest. If the function is the celebrated Weierstrass function, it follows from some of our results that the set cord derivates at any point coincides with the extended real line.

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Steen Pedersen. Joseph P. Sjoberg. "Sequential derivatives." Real Anal. Exchange 46 (1) 191 - 206, 2021. https://doi.org/10.14321/realanalexch.46.1.0191

Information

Published: 2021
First available in Project Euclid: 14 October 2021

Digital Object Identifier: 10.14321/realanalexch.46.1.0191

Subjects:
Primary: 26A24 , 26A27
Secondary: 26A06 , 47B25

Keywords: cord derivative , generalized derivative , non-differentiable function , nowhere-differentiable function , Real function , secant derivative , sequential derivative , Weierstrass function

Rights: Copyright © 2021 Michigan State University Press

Vol.46 • No. 1 • 2021
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