Another characterization of convexity for set-valued maps

We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of P...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 20; no. 3-4; pp. 341 - 351
Main Author: Sach, Pham Huu
Format: Journal Article
Language:English
Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1999
Taylor & Francis
Subjects:
coderivative
convexity
Exact sciences and technology
Mathematical analysis
Mathematics
Measure and integration
Primary:26 A 24
Primary:26 B 25
Primary:26 E 25
Real functions
Sciences and techniques of general use
Secondary:28 A 15
Set-valued map
Convex hull
Clark Rockafellar subdifferential
Necessary and sufficient condition
Coderivative
Set valued map
Frechet derivative
Convexity
Banach space
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot . A detailed discussion is devoted to special cases when the contingent, the Fréchet and the Clarke-Rockafellar subdifFerentials Sixe used as this abstract subdifferential.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630569908816896