共查询到20条相似文献,搜索用时 109 毫秒
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本文研究了广义度量空间(A)型和(B)型弱F压缩的问题.利用迭代的方法,获得了在完备广义度量空间关于这些映射的不动点定理的结果,推广了完备度量空间F压缩的一些结果. 相似文献
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引进了一类混合型膨胀映射族,并在锥度量空间上证明了此类映射族具有唯一公共不动点的定理,同时给出了相应的不动点定理,推广和改进了文献中关于第I膨胀映射的相应的公共不动点和不动点定理. 相似文献
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本文证明锥b-度量空间中关于扩张映射的一些不动点定理,没有考虑映射的连续性和锥的正规性.其结果不仅推广了锥度量空间,度量空间和b-度量空间中的相关结果,而且也延拓和补充了先前的一些结果.此外,我们给出几个例子验证了其结论. 相似文献
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本文介绍了bv(s)-度量空间中广义ψ-Geraghty压缩的概念.利用不动点理论的方法获得了在完备bv(s)-度量空间中关于此压缩映射的不动点定理并且得到一些推论.此外,给出了一个支持本文主要结果的例子. 相似文献
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M. V. Korobkov 《Siberian Mathematical Journal》2008,49(3):436-451
We say that a domain U ? ?n is uniquely determined from the relative metric of its Hausdorff boundary (the relative metric is the extension by continuity of the intrinsic metric of the domain to the boundary) if every domain V ? ?n with the Hausdorff boundary isometric in the relative metric to the Hausdorff boundary of U is isometric to U too (in the Euclidean metrics). In this article we state some necessary and sufficient conditions for a plane domain to be uniquely determined from the relative metric of its Hausdorff boundary. 相似文献
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M. V. Korobkov 《Siberian Advances in Mathematics》2010,20(4):256-284
We say that a domain U ⊂ ℝ
n
is uniquely determined by the relative metric (which is the extension by continuity of the intrinsic metric of the domain
on its boundary) of its Hausdorff boundary if any domain V ⊂ ℝ
n
such that its Hausdorff boundary is isometric in the relative metric to the Hausdorff boundary of U, is isometric to U in the Euclidean metric. In this paper, we obtain the necessary and sufficient conditions for the uniqueness of determination
of a domain by the relative metric of its Hausdorff boundary. 相似文献
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We define a natural semi-definite metric on quasi-fuchsian space, derived from geodesic current length functions and Hausdorff
dimension, that extends the Weil–Petersson metric on Teichmüller space. We use this to describe a metric on Teichmüller space
obtained by taking the second derivative of Hausdorff dimension and show that this metric is bounded below by the Weil–Petersson
metric. We relate the change in Hausdorff dimension under bending along a measured lamination to the length in the Weil–Petersson
metric of the associated earthquake vector of the lamination.
Martin Bridgeman research supported in part by NSF grant DMS 0305634. Edward C. Taylor research supported in part by NSF grant
DMS 0305704. 相似文献
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O. S. Malysheva 《Moscow University Mathematics Bulletin》2018,73(5):182-189
Non–empty compact subsets of the Euclidean space located optimally (i.e., the Hausdorff distance between them cannot be decreased) are studied. It is shown that if one of them is a single point, then it is located at the Chebyshev center of the other one. Many other particular cases are considered too. As an application, it is proved that each three–point metric space cari be isometrically embedded into the orbit space of the group of proper motions acting on the compact subsets of the Euclidean space. In addition, it is proved that for each pair of optimally located compact subsets all intermediate compact sets in the sense of Hausdorff metric are also intermediate in the sense of Euclidean Gromov–Hausdorff metric. 相似文献
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S. Jurina N. MacGregor A. Mitchell L. Olsen A. Stylianou 《Aequationes Mathematicae》2018,92(4):709-735
We study the Hausdorff and packing measures of typical compact metric spaces belonging to the Gromov–Hausdorff space (of all compact metric spaces) equipped with the Gromov–Hausdorff metric. 相似文献
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《Stochastic Processes and their Applications》2020,130(6):3842-3864
In this work, it is proved that the set of boundedly-compact pointed metric spaces, equipped with the Gromov–Hausdorff topology, is a Polish space. The same is done for the Gromov–Hausdorff–Prokhorov topology. This extends previous works which consider only length spaces or discrete metric spaces. This is a measure theoretic requirement to study random boundedly-compact pointed (measured) metric spaces, which is the main motivation of this work. In particular, this provides a unified framework for studying random graphs, random discrete spaces and random length spaces. The proofs use a generalization of the classical theorem of Strassen, presented here, which is of independent interest. This generalization provides an equivalent formulation of the Prokhorov distance of two finite measures, having possibly different total masses, in terms of approximate couplings. A Strassen-type result is also provided for the Gromov–Hausdorff–Prokhorov metric for compact spaces. 相似文献
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P.E. Kloeden 《Fuzzy Sets and Systems》1980,4(2):193-201
A metric is defined on a space of functions from a locally compact metric space X into the unit interval I in terms of the Hausdorff metric distance between their compact supported endographs in X × I. Convergence in this metric is shown to be equivalent to the conjunction of the Hausdorff metric convergence of supports in X and two conditions involving numerical values of the functions. The space of nonempty compact subsets of X with the Hausdorff metric is imbedded in the above function space by the characteristic function on subsets of X. Applications of these results to fuzzy subsets of X and fuzzy dynamical systems on X are indicated. 相似文献
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For every Hausdorff function we construct a compact metric space of finite positive weak-packing measure. Also we prove that for every non-doubling Hausdorff function there exists a compact metric space on which the packing and weak-packing measures are not equivalent. 相似文献
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《随机分析与应用》2013,31(4):1067-1083
Abstract The strong laws of large numbers with the convergence in the sense of the uniform Hausdorff metric for stationary sequences of random upper semicontinuous functions is established. This approach allows us to deduce many results on the convergence in uniform Hausdorff metric of random upper semicontinuous functions from the relevant results on real-valued random variables that appear as their support functions. 相似文献
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Sibe Marde
i 《Topology and its Applications》1988,30(3):291-306
The well-known factorization theorems for covering dimension dim and compact Hausdorff spaces are here established for the cohomological dimension dim
using a new characterization of dim
In particular, it is proved that every mapping f: X → Y from a compact Hausdorff space X with
to a compact metric space Y admits a factorization f = hg, where g: X → Z, h: Z → Y and Z is a metric compactum with
. These results are applied to the well-known open problem whether
. It is shown that the problem has a positive answer for compact Hausdorff spaces X if and only if it has a positive answer for metric compacta X. 相似文献