Minimal convex uscos and monotone operators on small sets

Title: Minimal convex uscos and monotone operators on small sets
Creator: Borwein, Jonathan; Fitzpatrick, Simon; Kenderov, Petàr
Relation: Canadian Journal of Mathematics Vol. 43, Issue 3, p. 461-476
Publisher Link: http://dx.doi.org/10.4153/CJM-1991-028-5
Publisher: University of Toronto Press
Resource Type: journal article
Date: 1991
Description: 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.
Subject: monotone operators; Banach spaces; Asplund spaces; Lipschitzian functions; minimal convex uscos
Identifier: http://hdl.handle.net/1959.13/1042541
Identifier: uon:14075
Identifier: ISSN:0008-414X
Language: eng
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