Affiliation:
1. Department of Mathematics, DePaul University, Chicago, IL 60614, USA
Abstract
Abstract
We provide three characterizations of the $n$th symmetric (Peano) derivative $f_{(n)}^{s}(x)$ in terms of symmetric generalized Riemann derivatives of a function $f$ at $x$ and a characterization of the $n$th Peano derivative $f_{(n)}(x)$ in terms of generalized Riemann derivatives of $f$ at $x$. The latter has been a conjecture by Ginchev, Guerragio, and Rocca since 1998.
Publisher
Oxford University Press (OUP)
Reference32 articles.
1. Generalizations of the Riemann derivative;Ash;Trans. Amer. Math. Soc.,1967
2. A characterization of the Peano derivative;Ash;Trans. Amer. Math. Soc.,1970
3. New definitions of continuity;Ash;Real Anal. Exchange,2014–2015
4. Quantum symmetric ${\mathrm{L}}^{\mathrm{p}}$ derivatives;Ash;Trans. Amer. Math. Soc.,2008
5. Multidimensional Riemann derivatives;Ash;Studia Math.,2016
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