共查询到19条相似文献,搜索用时 46 毫秒
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《数学学报》2020,(5)
本文研究TVS-锥度量空间中的统计收敛以及TVS-锥度量空间的统计完备性.令(X,E,P,d)表示一个TVS-锥度量空间.利用定义在有序Hausdorff拓扑向量空间E上的Minkowski函数ρ,证明了在X上存在一个通常意义下的度量d_ρ,使得X中的序列(x_n)在锥度量d意义下统计收敛到x∈X,当且仅当(x_n)在度量d_ρ意义下统计收敛到x.基于此,我们证明了任意一个TVS-锥统计Cauchy序列是几乎处处TVS-锥Cauchy序列,还证明了任意一个TVS-锥统计收敛的序列是几乎处处TVS-锥收敛的.从而,TVS-锥度量空间(X,d)是d-完备的,当且仅当它是d-统计完备的.基于以上结论,通常度量空间中统计收敛的许多性质都可以平行地推广到锥度量空间中统计收敛的情形. 相似文献
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在TVS-锥度量空间概念的基础上,建立了TVS-锥度量空间的若干理论,并运用这些理论,对满足不同条件的扩张型映射,采用不同的迭代方法,得到了TVS-锥度量空间中扩张映射新的不动点定理,结果是度量空间中某些经典结果在锥度量空间的进一步推广和发展. 相似文献
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赵云鹏 《应用泛函分析学报》2020,(1):72-76
在完备的TVS-锥度量空间中研究了经典的扩张型映射的公共不动点的存在性及唯一性,所得结果推广了一些已知的重要结论,将扩张映射公共不动点的研究从锥度量空间(Banach-锥)发展到TVS-锥度量空间. 相似文献
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在非完备的拓扑线性空间值锥度量空间上得到了新的满足某种Lipschitz型条件的四个映射的唯一公共不动点定理并给出了一些推论.所得结果推广和改进了文献中一些已知结论. 相似文献
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在TVS-值锥度量空间上给出若干可数个满足拟-Lipschitz条件的满映射族的唯一公共不动点的存在性定理.主要结论推广和改进了文献中的一些相应结论. 相似文献
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本文在G-锥度量空间中引入弱相容映射,得到G-锥度量空间在自映射压缩条件下的不动点定理和在弱相容自映射压缩条件下的公共不动点定理,并通过迭代法证明了这两个主要定理. 相似文献
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《数学季刊》2016,(4)
A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature. 相似文献
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Abstract In this article, we introduce the concepts of strongly statistically convergent sequence and strong statistically Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong statistical limit points and the strong statistical cluster points of a sequence in this space and investigate the relations between these concepts. 相似文献
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In this study, the concept of a statistically D-bounded sequence in a probabilistic normed (PN) space endowed with the strong topology is introduced and its basic properties are investigated. It is shown that a strongly statistically convergent sequence and a strong statistically Cauchy sequence are statistically D-bounded under certain conditions. A sequence which goes far away from the limit point infinitely many times and presents random deviations in a PN space may be handled with the tools of strong statistical convergence and statistical D-boundedness. 相似文献
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The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric. Two particular cases of statistical data are defined. The existence and uniqueness of a nonlinear connection corresponding to these classes is proved. Two Koszul tensors are introduced in accordance with the Riemannian approach. As applications, the authors treat the Finslerian (α, β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model. 相似文献
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Some topological properties of cone metric spaces are discussed and proved that every cone metric space (X, d) is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection. 相似文献
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In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of -statistical convergence. A sequence xis -statistically convergent to a set Cif Cis a minimal closed set such that for every > 0 the set
has density zero. It is shown that every statistically bounded sequence is -statistically convergent. Moreover if a sequence is -statistically convergent then the limit set is a set of statistical cluster points. 相似文献