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A criterion of $\varGamma $-nullness and differentiability of convex and quasiconvex functions

Volume 227 / 2015

Jaroslav Tišer, Luděk Zajíček Studia Mathematica 227 (2015), 149-164 MSC: Primary 46G05; Secondary 49J50. DOI: 10.4064/sm227-2-5

Abstract

We introduce a criterion for a set to be $\varGamma $-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 $\varGamma $-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.

Authors

  • Jaroslav TišerDepartment of Mathematics
    Faculty of Electrical Engineering
    Czech Technical University
    Technická 2
    166 27 Praha 6, Czech Republic
    e-mail
  • Luděk ZajíčekCharles University
    Faculty of Mathematics and Physics
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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