The Strong Conical Hull Intersection Property and the Perturbation Property in Approximation Theory

• Main Authors: CHUANG,YI-HSIANG, 莊逸祥
• Other Authors: 楊南屏
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/06170012735037712461

碩士 === 輔仁大學 === 數學系研究所 === 94 === Let X be a real Hilbert space, C be a closed convex subset, and Hi := fx . X jhx, hii. bi} (i =1, 2;:::;m) be a finite collection of half-spaces. Assuming := C(Tm 1 Hi) is not empty, the problem of characterizing the best approximation from K to any x . X is considered. Then strong conical hull intersection property (abbreviatedly, strong CHIP) of fC, H1;:::;Hm} and perturbation property are introduced. According to the strong CHIP or perturbation property, an element x0 . K satis es PK (x)= x0 = PC (x . Pm 1 ihi) for some scalars i . 0 with i[hx0;hii. bi] = 0 for each i. Under certain circumstances, we discuss some results of the perturbation property from K := C Hei + C Hbi , where C is a closed convex set, fHe1;:::, Hem} and fHb1;:::, Hbm} are collections of half-spaces.