Minimal convex uscos and monotone operators on small sets

Borwein, Jonathan M. and Fitzpatrick, Simon and Kenderov, Petàr (1991) Minimal convex uscos and monotone operators on small sets. Canadian Journal of Mathematics , 43 (3). pp. 461-476.

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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.

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 18 Feb 2015 14:51
Last Modified: 18 Feb 2015 14:51

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