On Asplund functions

Wee-Kee Tang

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 121-132
  • ISSN: 0010-2628

Abstract

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A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.

How to cite

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Tang, Wee-Kee. "On Asplund functions." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 121-132. <http://eudml.org/doc/248382>.

@article{Tang1999,
abstract = {A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.},
author = {Tang, Wee-Kee},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fréchet differentiability; convex functions; Asplund spaces; Fréchet differentiability; convex function; Asplund space},
language = {eng},
number = {1},
pages = {121-132},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Asplund functions},
url = {http://eudml.org/doc/248382},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Tang, Wee-Kee
TI - On Asplund functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 121
EP - 132
AB - A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.
LA - eng
KW - Fréchet differentiability; convex functions; Asplund spaces; Fréchet differentiability; convex function; Asplund space
UR - http://eudml.org/doc/248382
ER -

References

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  13. Preiss D., Zajíček D., Fréchet differentiability of convex functions in Banach space with separable duals, Proc. Amer. Math. Soc. 91 (1984), 202-204. (1984) MR0740171
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  16. Tang W.-K., On Fréchet differentiability of convex functions on Banach spaces, Comment. Math. Univ. Carolinae 36 (1995), 249-253. (1995) Zbl0831.46045MR1357526
  17. Tang W.-K., Sets of differentials and smoothness of convex functions, Bull. Austral. Math. Soc. 52 (1995), 91-96. (1995) Zbl0839.46008MR1344263
  18. Yost D., Asplund spaces for beginners, Acta Univ. Carolinae 34 (1993), 159-177. (1993) Zbl0815.46022MR1282979

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