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1.
首先给出赋范线性空间中的非空集合C的逼近紧性的等价描述. 如所周知, 如果C是Banach空间X中的一个逼近紧的半Chebyshev闭集, 那么由X到C的度量投影算子πc是连续的. 当X是中点局部一致凸的Banach 空间, 利用Banach空间几何的技巧证得: C的逼近紧性对投影算子πc的连续性也是必要的. 利用这个一般结论给出: 当T是由逼近紧且严格凸的Banach空间$X$到中点局部一致凸Banach空间Y的有界线性算子时, T有连续的Morse-Penrose度量广义逆T+$的充分必要条件.  相似文献   

2.
本文定义了近可凹的Banach 空间. 利用Banach 空间几何技巧证得: X 是逼近紧的当且仅当(1) X 是近可凹的; (2) X 是近严格凸的. 还证明了如果Banach 空间X 是近可凹的, 则对任意闭凸集C, 度量投影算子PC 是上半连续的. 最后作者给出了近可凹性在广义逆理论中的应用.  相似文献   

3.
非自反Banach空间中的度量投影   总被引:1,自引:1,他引:0       下载免费PDF全文
该文给出非自反Banach空间中一类超平面上度量投影的表达式.在近严格凸Banach空间中,研究了它们的连续性.对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果.  相似文献   

4.
(C—K)性质的特征   总被引:13,自引:0,他引:13  
该文绘出(C-K),K=Ⅰ,Ⅱ,Ⅲ正性质的一些充要条件,从而我们得到:如果Banach空间X有(C一Ⅲ)((C-Ⅱ);(C-Ⅰ)性质,则对X的任意赋范集AU(X*),单位球面S(X)上的σ(X,A)拓朴与弱拓扑(范数拓扑)等价且X近非常凸(近强凸;强凸).  相似文献   

5.
关于度量投影的连续性   总被引:10,自引:1,他引:9  
王建华 《应用数学》1995,8(1):80-84
本文引入的Banach空间的(C-I)、(C-Ⅱ),(C-Ⅲ)等几何性质,证明了如下结果。设M是Banach空间的逼近凸子集,如果Banach空间有性质(C-I),(C-Ⅱ)(C-Ⅲ),则度量投影PM连续(范数-范数上半连续,范数-弱上半连续)。这些结果推广了文(4,7,8)相应的定理。最近,D.Kutzarova,Bor-Luh Lin等引入了一些新的凸性空间,本文还研究了这些凸性空间中度量投影  相似文献   

6.
方习年 《数学杂志》2001,21(1):38-44
本文通过引入B-NUC Banach空间及WB性质,进一步研究Banach-Saks性质(BSP)与近一致凸及紧完全凸性之间的关系。得到以下主要结果。1)Banach空间X具有WB性质当且仅当X具有WBanach-Saks性质(WBSP);2)X是B-NUC空间当且仅当X是具BSP的NUC空间;3)若X具BSP及(H)性质,则X是CωR空间(紧完全ω-凸空间)。  相似文献   

7.
该文给出Banach空间X的对偶空间X~*中闭超平面上度量投影的表达式,并在Banach空间中研究了闭超平面上度量投影的连续性.  相似文献   

8.
积分凸性及其应用   总被引:1,自引:0,他引:1       下载免费PDF全文
该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集,下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.  相似文献   

9.
吴伟志 《数学研究》1998,31(3):244-247
讨论了赋范空间中度量投影的收敛性.得到了在局部紧集控制下.Chebyshov凸集序列的度量投影的收敛性与K-M收敛,Wlisman收敛和Kuratowskl收敛都等价.本文的结论完善了M.Tsukada在[1]和[2]的结果.  相似文献   

10.
非常极凸空间的推广及其对偶概念   总被引:1,自引:1,他引:0  
本文研究了k非常极凸和k非常极光滑空间的问题.利用Banach空间理论的方法,证明了k非常极凸空间和k非常极光滑空间是一对对偶概念,并且k非常极凸空间(k非常极光滑空间)是严格介于k一致极凸空间和k非常凸空间(k一致极光滑空间和k非常光滑空间)之间的一类新的Banach空间,得到了k非常极凸空间和k非常极光滑空间的若干等价刻画以及k非常极凸(k非常极光滑性)与其它凸性(光滑性)之间的蕴涵关系,推广了非常极凸空间和非常极光滑空间,完善了k非常极凸空间及其对偶空间的研究.  相似文献   

11.
Criteria for nearly strict convexity of Musielak-Orlicz-Bochner function spaces equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz-Bochner function spaces generated by strictly convex Banach space, nearly strict convexity and strict convexity are equivalent.  相似文献   

12.
A convex function defined on an open convex set of a finite-dimensional space is known to be continuous at every point of this set. In fact, a convex function has a strengthened continuity property. The notion of strong continuity is introduced in this study to show that a convex function has this property. The proof is based on only the definition of convexity and Jensen’s inequality. The definition of strong continuity involves a constant (the constant of strong continuity). An unimprovable value of this constant is given in the case of convex functions. The constant of strong continuity depends, in particular, on the form of a norm introduced in the space of arguments of a convex function. The polyhedral norm is of particular interest. It is straightforward to calculate the constant of strong continuity when it is used. This requires a finite number of values of the convex function.  相似文献   

13.
In this paper, we show a relationship between strictly convexity of type (I) and (II) defined by Takahashi and Talman, and we prove that any uniformly convex metric space is strictly convex of type (II). Continuity of the convex structure is also shown on a compact domain. Then, we prove the existence of a minimum point of a convex, lower semicontinuous and d-coercive function defined on a nonempty closed convex subset of a complete uniformly convex metric space. By using this property, we prove fixed point theorems for (α, β)-generalized hybrid mappings in uniformly convex metric spaces. Using this result, we also obtain a common fixed point theorem for a countable commutative family of (α, β)-generalized hybrid mappings in uniformly convex metric spaces. Finally, we establish strong convergence of a Mann type iteration to a fixed point of (α, β)-generalized hybrid mapping in a uniformly convex metric space without assuming continuity of convex structure. Our results can be applied to obtain the existence and convergence theorems for (α, β)-generalized hybrid mappings in Hilbert spaces, uniformly convex Banach spaces and CAT(0) spaces.  相似文献   

14.
SupportingFunctionsandTheDifferentiabilitiesoftheNormsonBanachSpaces¥WangJiangen(王建根)(LuoyangTeacher'sCollege)Abstract:Inthis...  相似文献   

15.
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [S. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comput. 196 (2008) 422–425] which was established for nonexpansive mappings.  相似文献   

16.
本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧-严格凸、紧-强凸、紧-一致凸及紧-非常凸等概念。并用对偶映射给出了Banach空间的两种新光滑性—紧-一致光滑与紧-非常光滑。然后特别研究了Banach空间的紧-非常凸与紧-非常光滑。此外还得到关于对偶映射的两个新结果。  相似文献   

17.
For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.  相似文献   

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