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

• Autorzy: Jaroslav Tišer , Luděk Zajíček
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 49J50: Fr\'echet and Gateaux differentiability
• 46G05: Derivatives

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 2
• Strony: 149-164

Daty

wydano

2015

Twórcy

autor

Jaroslav Tišer

• Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Praha 6, Czech Republic

autor

Luděk Zajíček

• Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/sm227-2-5