Differentiability of Peano derivatives
HTML articles powered by AMS MathViewer
- by Andreas Fischer PDF
- Proc. Amer. Math. Soc. 136 (2008), 1779-1785 Request permission
Abstract:
Peano differentiability is a notion of higher-order Fréchet differentiability. H. W. Oliver gave sufficient conditions for the $m$th Peano derivative to be a Fréchet derivative in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.References
- Saheb Dayal, Higher Fréchet and discrete Gateaux differentiability of $n$-convex functions on Banach spaces, Functional analysis and operator theory (New Delhi, 1990) Lecture Notes in Math., vol. 1511, Springer, Berlin, 1992, pp. 154–171. MR 1180760, DOI 10.1007/BFb0093809
- Krzysztof Kurdyka and Wiesław Pawłucki, Subanalytic version of Whitney’s extension theorem, Studia Math. 124 (1997), no. 3, 269–280. MR 1456425, DOI 10.4064/sm-124-3-269-280
- H. William Oliver, The exact Peano derivative, Trans. Amer. Math. Soc. 76 (1954), 444–456. MR 62207, DOI 10.1090/S0002-9947-1954-0062207-1
- Peano, G., Sulla formula di Taylor. (Italian) Torino Atti XXVII. 40-46. (1891).
Additional Information
- Andreas Fischer
- Affiliation: Department of Mathematics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan S7N 5E6, Canada
- Email: el.fischerandreas@web.de
- Received by editor(s): October 28, 2005
- Received by editor(s) in revised form: April 17, 2006
- Published electronically: December 18, 2007
- Additional Notes: The author’s research was supported by EC-IHP-Network RAAG (Contract-No: HPRN-CT-2001-00271)
- Communicated by: David Preiss
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1779-1785
- MSC (2000): Primary 26B05
- DOI: https://doi.org/10.1090/S0002-9939-07-09320-3
- MathSciNet review: 2373608