SOME GENERALIZATIONS OF THE WEIERSTRASS THEOREM

被引:7
|
作者
Amini-Harandi, A. [1 ,2 ]
Fakhar, M. [1 ,2 ]
Hajisharifi, H. R. [3 ]
机构
[1] Univ Isfahan, Dept Math, Esfahan 81745163, Iran
[2] Inst Res Fundamental Sci IPM, Sch Math, POB 193955746, Tehran, Iran
[3] Khansar Fac Math & Comp Sci, Dept Math, POB 87916854163, Khansar, Iran
关键词
Weierstrass's theorem; qrgi functions; transfer weakly lower continuous; nearly quasi-convex functions; noncoercive functions; reflexive Banach spaces; EXISTENCE; OPTIMIZATION;
D O I
10.1137/15M1054997
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main goal of this paper is to obtain a generalization of the Weierstrass theorem for transfer weakly lower continuous functions on noncompact topological spaces. To achieve this goal, the notion of a quasi-regular-global-inf (qrgi) function on a topological space is introduced, some equivalent statements are given, and a Weierstrass-type theorem for such functions is proved. Moreover, the well-posedness of the minimization problem for regular-global-inf (rgi) and qrgi functions is studied. Furthermore, in the setting of reflexive Banach spaces the existence of global minimum points of noncoercive qrgi and transfer weakly lower continuous functions are investigated. We also introduce the concept of nearly quasi-convexity of a function, as a generalization of the quasi-convexity notion, and present a result on the minimization problem of these functions.
引用
收藏
页码:2847 / 2862
页数:16
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