Differentiation of n-convex functions

H. Fejzić, R. E. Svetic, and C. E. Weil. "Differentiation of n-convex functions." Fundamenta Mathematicae 209.1 (2010): 9-25. <http://eudml.org/doc/282761>.

@article{H2010,
abstract = {The main result of this paper is that if f is n-convex on a measurable subset E of 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 nth approximate Peano derivative of f almost everywhere.},
author = {H. Fejzić, R. E. Svetic, C. E. Weil},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {9-25},
title = {Differentiation of n-convex functions},
url = {http://eudml.org/doc/282761},
volume = {209},
year = {2010},
}

TY - JOUR
AU - H. Fejzić
AU - R. E. Svetic
AU - C. E. Weil
TI - Differentiation of n-convex functions
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 1
SP - 9
EP - 25
AB - The main result of this paper is that if f is n-convex on a measurable subset E of 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 nth approximate Peano derivative of f almost everywhere.
LA - eng
UR - http://eudml.org/doc/282761
ER -