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Properties of the trajectories of set-valued integrals in banach spaces

Published online by Cambridge University Press:  17 April 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
University of California1015 Department of MathematicsDavis, CA 95616United States of America
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Abstract

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Let F: T → 2x \ {} be a closed-valued multifunction into a separable Banach space X. We define the sets and We prove various convergence theorems for those two sets using the Hausdorff metric and the Kuratowski-Mosco convergence of sets. Then we prove a density theorem of CF and a corresponding convexity theorem for F(·). Finally we study the “differentiability” properties of K(·). Our work extends and improves earlier ones by Artstein, Bridgland, Hermes and Papageorgiou.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 271 - 281
Copyright
Copyright © Australian Mathematical Society 1990

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