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The implications for differentiability of a weak index of non-compactness

Published online by Cambridge University Press:  17 April 2009

John R. Giles  and
Warren B. Moors
John R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
Warren B. Moors
Affiliation:
Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
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In a recent paper the authors showed that certain set-valued mappings from a Baire space into subsets of a Banach space which have a continuity property defined in terms of Kuratowski's index of non-compactness have inherent single-valued properties. Here we generalise the continuity property to one defined in terms of a weak index of non-compactness and we show that this wider class of set-valued mappings also has significant implications for the differentiability of convex functions on Banach spaces.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 75 - 91
Copyright
Copyright © Australian Mathematical Society 1993

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