# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Differentiation of $n$-convex functions

### Tom 209 / 2010

Fundamenta Mathematicae 209 (2010), 9-25 MSC: Primary 26A24; Secondary 26A51, 26A12, 26C99. DOI: 10.4064/fm209-1-2

#### Streszczenie

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.

#### Autorzy

• H. FejzićDepartment of Mathematics
California State University
San Bernardino, CA 92407, U.S.A.
e-mail
• R. E. Svetic2022 N. Nevada St.
Chandler, AZ 85225, U.S.A.
• C. E. WeilDepartment of Mathematics
Michigan State University
East Lansing, MI 48824-1027, U.S.A.
e-mail

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