کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9496009 | 1335208 | 2005 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Slice-continuous sets in reflexive Banach spaces: convex constrained optimization and strict convex separation
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Slice-continuous sets in reflexive Banach spaces: convex constrained optimization and strict convex separation Slice-continuous sets in reflexive Banach spaces: convex constrained optimization and strict convex separation](/preview/png/9496009.png)
چکیده انگلیسی
The concept of continuous set has been used in finite dimension by Gale and Klee and recently by Auslender and Coutat. Here, we introduce the notion of slice-continuous set in a reflexive Banach space and we show that the class of such sets can be viewed as a subclass of the class of continuous sets. Further, we prove that every nonconstant real-valued convex and continuous function, which has a global minima, attains its infimum on every nonempty convex and closed subset of a reflexive Banach space if and only if its nonempty level sets are slice-continuous. Thereafter, we provide a new separation property for closed convex sets, in terms of slice-continuity, and conclude this article by comments.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 223, Issue 1, 1 June 2005, Pages 179-203
Journal: Journal of Functional Analysis - Volume 223, Issue 1, 1 June 2005, Pages 179-203
نویسندگان
Emil Ernst, Michel Théra, Constantin ZÄlinescu,