Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T16:14:16.557Z Has data issue: false hasContentIssue false

Upper Semi-Continuity of Subdifferential Mappings

Published online by Cambridge University Press:  20 November 2018

David A. Gregory*
Affiliation:
Department of Mathematics and Statistics Queen's University, Kingston, Ontario K7L 3N6
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.

Characterizations of the upper semi-continuity of the subdifferential mapping of a continuous convex function are given.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Asplund, E. and Rockafellar, R. T., Gradients of convex functions, Trans. A.M.S., 139 (1969), 443-467.Google Scholar
2. Giles, J. R., Gregory, D. A., and Brailey, Sims, Geometrical implications of upper semicontinuity of the duality mapping on a Banach space, to appear in Pacific J. Math.Google Scholar
3. Holmes, R. B., Geometric functional analysis and its applications, Springer-Verlag, New York (1975).Google Scholar
4. Kenderov, P., Semi-continuity of set-valued monotone mappings, Fund. Math. 88 (1975), 61-69.Google Scholar
5. Smulian, V. L., Sur la derivabilit? de la norme dans Vespace de Banach, Dokl. Akad. Nauk.SSSR., 27 (1940), 643-648.Google Scholar
6. Giles, J. R., Strong differentiability of the norm and rotundity of the dual, to appear.Google Scholar