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Characterisation of drop and weak drop properties for closed bounded convex sets

Published online by Cambridge University Press:  17 April 2009

J.R. Giles  and
Denka N. Kutzarova
J.R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
Denka N. Kutzarova
Affiliation:
Institute of Mathematics Bulgarian Academy of Sciences, 1090 Sofia, Bulgaria and The University of Missouri-Columbia, Columbia Missouri 65211, United States of America
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Abstract

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Modifying the concept underlying Daneš' drop theorem, Rolewicz introduced the notion of the drop property of a norm which was later generalised to the weak drop property of a norm. Kutzarova extended the discussion to consider the drop property for closed bounded convex sets. Here we characterise the drop and weak drop properties for such sets by upper semi-continuous and compact valued subdifferential mappings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 377 - 385
Copyright
Copyright © Australian Mathematical Society 1991

References

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