Differentiation of $n$-convex functions

Tom 209 / 2010

H. Fejzić, R. E. Svetic, C. E. Weil 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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