A criterion of Γ-nullness and differentiability of convex and quasiconvex functions

Jaroslav Tišer, and Luděk Zajíček. "A criterion of Γ-nullness and differentiability of convex and quasiconvex functions." Studia Mathematica 227.2 (2015): 149-164. <http://eudml.org/doc/285865>.

@article{JaroslavTišer2015,
abstract = {We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.},
author = {Jaroslav Tišer, Luděk Zajíček},
journal = {Studia Mathematica},
keywords = {differentiability; -null sets; convex function; quasiconvex function; Hadamard differentiability},
language = {eng},
number = {2},
pages = {149-164},
title = {A criterion of Γ-nullness and differentiability of convex and quasiconvex functions},
url = {http://eudml.org/doc/285865},
volume = {227},
year = {2015},
}

TY - JOUR
AU - Jaroslav Tišer
AU - Luděk Zajíček
TI - A criterion of Γ-nullness and differentiability of convex and quasiconvex functions
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 2
SP - 149
EP - 164
AB - We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.
LA - eng
KW - differentiability; -null sets; convex function; quasiconvex function; Hadamard differentiability
UR - http://eudml.org/doc/285865
ER -