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Minimal Convex Uscos and Monotone Operators on Small Sets

Published online by Cambridge University Press:  20 November 2018

Jonathan Borwein ,
Simon Fitzpatrick  and
Petàr Kenderov
Jonathan Borwein
Affiliation:
Dalhousie University Halifax, NS B3H 3J5
Simon Fitzpatrick
Affiliation:
Department of Auckland University of Auckland 38 Princess Street Aukland, New Zealand
Petàr Kenderov
Affiliation:
University of Sophia Department of Mathematics Anton Ivanov. Str. 5. Sophia 1126 Bulgaria
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Abstract

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We generalize the generic single-valuedness and continuity of monotone operators defined on open subsets of Banach spaces of class (S) and Asplund spaces to monotone operators defined on convex subsets of such spaces which may even fail to have non-support points. This yields differentiability theorems for convex Lipschitzian functions on such sets. From a result about minimal convex uscos which are densely single-valued we obtain generic differentiability results for certain Lipschitzian realvalued functions.

Keywords

46G057H0754C5054C65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 461 - 476
Copyright
Copyright © Canadian Mathematical Society 1991

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