A property of Peano derivatives in several variables
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- by Hajrudin Fejzić and Clifford E. Weil
- Proc. Amer. Math. Soc. 141 (2013), 2411-2417
- DOI: https://doi.org/10.1090/S0002-9939-2013-11529-7
- Published electronically: March 22, 2013
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Abstract:
Let $f$ be a function of several variables that is $n$ times Peano differentiable. Andreas Fischer proved that if there is a number $M$ such that $f_{\boldsymbol {\alpha } } \ge M$ or $f_{\boldsymbol {\alpha } } \le M$ for each $\boldsymbol {\alpha }$, with $\left | \boldsymbol {\alpha } \right | = n$, then $f$ is $n$ times differentiable in the usual sense. Here that result is improved to permit the type of one-sided boundedness to depend on $\boldsymbol {\alpha }$.References
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Bibliographic Information
- Hajrudin Fejzić
- Affiliation: Department of Mathematics, California State University, San Bernardino, California 92407-2397
- Email: hfejzic@csusb.edu
- Clifford E. Weil
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
- Email: weil@math.msu.edu
- Received by editor(s): August 13, 2011
- Received by editor(s) in revised form: October 20, 2011
- Published electronically: March 22, 2013
- Additional Notes: The first author was supported in part by CSUSB 2011 Summer Research Grant
- Communicated by: Tatiana Toro
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2411-2417
- MSC (2010): Primary 26B05, 26B35
- DOI: https://doi.org/10.1090/S0002-9939-2013-11529-7
- MathSciNet review: 3043022