共查询到20条相似文献,搜索用时 93 毫秒
1.
常曲率空间中有限点集的两类几何不等式 总被引:1,自引:1,他引:0
应用距离几何的理论与方法,研究了n维常曲率空间中有限点集的一些几何度量之间关系,建立了常曲率空间中有限点集的两类几何不等式,推广了已有的结果. 相似文献
2.
本文用代数方法建立了n维球面型空间Sn(K)和n维双曲空间Hn(K)中有限点集的点与点两两之间之距离的一类几何不等式,本文还建立了n维欧氏空间En中共球有限点集的一类几何不等式.作为本文结果的应用,简洁地得出[3]中的一个重要结果,并得出En中有限点集的两个几何不等式 相似文献
3.
伪轨跟踪与伪移位不变集 总被引:4,自引:0,他引:4
杨润生 《数学年刊A辑(中文版)》1997,(5)
本文证明了对于具有伪轨跟踪性质的紧致度量空间上的连续满射f,存在某个正整数n,有相对于fn的伪移位不变集的充要条件是存在非回归点的链回归点,或是存在非几乎周期点的回归点 相似文献
4.
拓扑空间X的覆盖列{P_i}_(i∈N)被称为空间X的点星网,若x∈X,则{st(x,P_i)}_(i∈N)是x在X中的网.本文刻画具有cs有限cs覆盖列的点星网的空间,并将其表示为度量空间在确定映射下的像.在假设集族性质β满足适当的条件下,证明对拓扑空间X下述条件相互等价:(1) X具有β且cs覆盖列的点星网.(2)X具有β且sn覆盖列的点星网.(3)X是Cauchy sn对称空间且具有σ-β的cs网.(4) X是Cauchy sn对称空间且具有σ-β的sn网.(5) X是度量空间的序列覆盖、π且σ-β映像.(6) X是度量空间的1序列覆盖、紧且σ-β映像.这些工作以局部有限集族与点有限集族为特例,拓展了从基到cs网的研究,丰富了映射与空间的相互分类思想. 相似文献
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实Hilbert空间中点到有限余维子空间的距离问题 总被引:2,自引:0,他引:2
本文讨论实Hilbert空间中一点到有限余维子空间的距离,将一点到超平面的距离公式推广到一点到余维n子空间M以及仿射集Q的距离公式,并对M或Q闭的情形表示出最佳逼近元。 相似文献
7.
共球有限点集的一类几何不等式 总被引:15,自引:0,他引:15
苏化明 《数学年刊A辑(中文版)》1994,(1)
本文建立了En中共球有限点集的一类几何不等式,作为其特例,可以得到n维单形的外接球半径与其子单形外接球半径之间的关系. 相似文献
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在三维空间中,由给定的n个点A1,A2,…,An组成的集合称为空间有限点集,简称点集,记作Ω={A1,A2,…,An}.在点集Ω={A1,A2,…,An}所在空间中任取一点P,满足等式PG=1n∑ni=1PAi的点G叫做点集Ω的重心.本文研究与空间有限点集的重心相关的两个轨迹问题.引理[1]设空间有限点集Ω={A1, 相似文献
10.
《数学的实践与认识》2018,(23)
仿造度量空间中链回归点的定义,给出了拓扑群作用下度量空间中G-链回归点的概念,并将度量空间中链回归点的一些结论,推广到拓扑群作用下度量空间中,得到如下结果:1)同胚伪等价映射f的G-链回点集等于它的逆映射f~(-1)的G-链回归点集;2)伪等价映射f的G-链回点集和G-链等价集对G强不变;3)同胚等价映射f的G-链回点集f对强不变.4)等价映射f限制在它的G-链回归点集上形成的G-链回归点集就是等价映射f在度量G-空间X上形成的G-链回归点集.这些结果丰富了拓扑群作用下度量空间中G-链回归点的理论. 相似文献
11.
本文建立乘积距离空间中集值与单值映像组的非线性压缩型公共不动点定理以及集值映像组公共不动点集的稳定性定理. 相似文献
12.
This paper studies the Fermat point in Hilbert spaces for a system of n distinct points. We prove the existence of the Fermat point and we determine its location in the convex hull of the given system of points. A new concept of Fermat point for a non–discrete set of points is introduced and there are proved similar results to discrete case. In the second part of this paper we give close form formulas of Fermat point for a system of 3 and 4 distinct points. We also describe some iterative methods to find the Fermat point for a system of more than 4 distinct points. 相似文献
13.
Francesco S. de Blasi Józef Myjak Simeon Reich Alexander J. Zaslavski 《Set-Valued and Variational Analysis》2009,17(1):97-112
We study nonexpansive set-valued maps in Banach and metric spaces. We are concerned, in particular, with the generic existence
and approximation of fixed points, as well as with the structure of fixed point sets.
相似文献
14.
Sylvester conjectured in 1893 and Gallai proved some 40 years later
that every finite set S of points in the plane includes two points
such that the line passing through them includes either no other point
of S or all other points of S. There are several ways of extending
the notion of lines from Euclidean spaces to arbitrary metric spaces.
We present one of them and conjecture that, with lines in metric
spaces defined in this way, the Sylvester--Gallai theorem generalizes
as follows: in every finite metric space there is a line consisting
of either two points or all the points of the space. Then we present
meagre evidence in support of this rash conjecture and finally we
discuss the underlying ternary relation of metric betweenness. 相似文献
15.
The Generic Stability of Fixed Points for Upper Semicontinuous Mappings in Hyperconvex Metric Spaces
The main goal of this paper is to establish the generic stability of Fan-Glicksberg type fixed points in hyperconvex metric spaces. In order to do so, we first give Fan-Glicksberg type fixed point theorem in hyperconvex metric spaces and then the generic stability of fixed points for upper semicontinuous set-valued mappings is obtained. Our generic stability results show that almost all of fixed points of upper semicontinuous set-valued mappings defined in compact hyperconvex metric spaces are stable in the sense of Baire category theory 相似文献
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Recently, Suzuki [T. Suzuki characterizes metric completeness, Proc. A generalized Banach contractlon principle that Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char- acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric O- completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point. 相似文献
18.
We study the existence of best proximity points for single-valued non-self mappings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results. 相似文献
19.
Moosa GABELEH 《数学物理学报(B辑英文版)》2014,(5):1661-1669
We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results. 相似文献
20.
On fuzzy metric spaces 总被引:1,自引:0,他引:1
In this paper we introduce the concept of a fuzzy metric space. The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number. Properties of fuzzy metric spaces are studied and some fixed point theorems are proved. 相似文献