Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T08:03:50.163Z Has data issue: false hasContentIssue false
  • English
  • Français

Sets of differentials and smoothness of convex functions

Published online by Cambridge University Press:  17 April 2009

Wee-Kee Tang
Wee-Kee Tang
Affiliation:
Department of MathematicsUniversity of AlbertaEdmontonCanadaT6G 2G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Approximation by smooth convex functions and questions on the Smooth Variational Principle for a given convex function f on a Banach space are studied in connection with majorising f by C1-smooth functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 91 - 96
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Asplund, E. and Rockafellar, R.T., ‘Gradients of convex functions’, Trans. Amer. Math. Soc. 139 (1968), 443–467.Google Scholar
[2]Beauzamy, B., Introduction to Banach spaces and their geometry, Math. Stud. 68 (North Holland, 1985).Google Scholar
[3]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Monographs and Surveys Pure Appl. Math. 64 (Pitman, 1993).Google Scholar
[4]Fabian, M., ‘On Projectional resolution of identity on the duals of certain Banach spaces’, Bull. Austral. Math Soc. 35 (1987), 363–371.CrossRefGoogle Scholar
[5]John, K. and Zizler, V., ‘Smoothness and its equivalents in weakly compactly generated Banach spaces’, J. Funt. Anal. 15 (1974), 161–166.Google Scholar
[6]Lindenstrauss, J. and Tzafrifi, L., Classical Banach spaces Vol. I, Ergebnisse der Mathematik und ihrer Grenzgebiete 92 (Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[7]Lindenstrauss, J. and Tzafrifi, L., Classical Banach spaces Vol. II, Ergebnisse der Mathematik und ihrer Grenzgebiete 97 (Springer-Verlag, Berlin, Heidelberg, New York, 1979).Google Scholar
[8]McLaughlin, D., Poliquin, R.A., Vanderwerff, J.D. and Zizler, V.E., ‘Second order Gateâux differentiable bump functions and approximations in Banach spaces’, Canad. J. Math 45 (1993), 612–625.CrossRefGoogle Scholar
[9]Phelps, R.R., Convex functions, monotone operators and differentiability, Lecture Notes in Mathematics 1364, (Second Edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[10]Tang, W-K., ‘On Fréchet differentiability of convex functions on Banach spaces’ (to appear).Google Scholar