| Summary: | 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.
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