Geodesic
Differentiation of $n$-convex functions
H. Fejzić 1   ; R. E. Svetic 2   ; C. E. Weil 3
1 Department of Mathematics California State University San Bernardino, CA 92407, U.S.A.
2 2022 N. Nevada St. Chandler, AZ 85225, U.S.A.
3 Department of Mathematics Michigan State University East Lansing, MI 48824-1027, U.S.A.
Fundamenta Mathematicae, Tome 209 (2010) no. 1, pp. 9-25 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The main result of this paper is that if $f$ is $n$-convex on a measurable subset $E$ of $\mathbb R$, then $f$ is $n-2$ times differentiable, $n-2$ times Peano differentiable and the corresponding derivatives are equal, and $f^{(n-1)}=f_{(n-1)}$ except on a countable set. Moreover $f_{(n-1)}$ is approximately differentiable with approximate derivative equal to the $n$th approximate Peano derivative of $f$ almost everywhere.
DOI : 10.4064/fm209-1-2
Keywords: main result paper n convex measurable subset mathbb n times differentiable n times peano differentiable corresponding derivatives equal n n except countable set moreover n approximately differentiable approximate derivative equal nth approximate peano derivative almost everywhere

H. Fejzić  1   ; R. E. Svetic  2   ; C. E. Weil  3

1 Department of Mathematics California State University San Bernardino, CA 92407, U.S.A.
2 2022 N. Nevada St. Chandler, AZ 85225, U.S.A.
3 Department of Mathematics Michigan State University East Lansing, MI 48824-1027, U.S.A. 
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H. Fejzić; R. E. Svetic; C. E. Weil. Differentiation of $n$-convex functions. Fundamenta Mathematicae, Tome 209 (2010) no. 1, pp. 9-25. doi: 10.4064/fm209-1-2

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