The integral convexity of sets and functionals in Banach spaces

By way of the Bochner integral of vector-valued functions, the integral convexity of sets and functionals and the concept of integral extreme points of sets are introduced in Banach spaces. The relations between integral convexity and convexity are mainly discussed, two integral extreme points theor...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2004-07, Vol.295 (1), p.211-224
Main Authors: Wang, Jian-Yong, Ma, Yu-Mei
Format: Article
Language:English
Subjects:
Bochner integral
Integral convex functional
Integral convex programming
Integral convex set
Integral extreme point
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Summary:By way of the Bochner integral of vector-valued functions, the integral convexity of sets and functionals and the concept of integral extreme points of sets are introduced in Banach spaces. The relations between integral convexity and convexity are mainly discussed, two integral extreme points theorems and their applications are obtained at last.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.03.033