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Generalized vs. ordinary differentiation


Authors: J. Marshall Ash, Stefan Catoiu and Marianna Csörnyei
Journal: Proc. Amer. Math. Soc. 145 (2017), 1553-1565
MSC (2010): Primary 26A24; Secondary 15A06, 26A27
DOI: https://doi.org/10.1090/proc/13224
Published electronically: December 15, 2016
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Abstract: There are difference quotients distinct from $ \displaystyle \frac {f(x+h)-f(x)}h$
which characterize differentiability. We find all of them.


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Additional Information

J. Marshall Ash
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: mash@depaul.edu

Stefan Catoiu
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: scatoiu@depaul.edu

Marianna Csörnyei
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: csornyei@math.uchicago.edu

DOI: https://doi.org/10.1090/proc/13224
Keywords: Derivatives, generalized derivatives, Peano derivatives, Riemann derivatives, $\mathcal{A}$-derivatives, generalized Riemann derivatives
Received by editor(s): March 17, 2016
Published electronically: December 15, 2016
Additional Notes: The second author’s research was partially supported by a 2014 Summer Research Grant from the Faculty and Development Program at DePaul University, College of Science and Health.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2016 American Mathematical Society