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The integral convexity of sets and functionals in Banach spaces |
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| Authors: | Jian-Yong Wang Yu-Mei Ma |
| Affiliation: | a Department of Mathematics, Changshu Institute of Technology, Jiangsu 215500, People's Republic of China b Department of Computer Science, Dalian National College, Liaoning 116600, People's Republic of China |
| Abstract: | 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. |
| Keywords: | Bochner integral Integral convex set Integral convex functional Integral extreme point Integral convex programming |
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