Some fixed point theorems on ordered cone metric spaces

In the present work, two fixed point theorems for self maps on ordered cone metric spaces are proved motivated by [7, L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007) 1468–1476] and [15, A. C. M. Ran and M. C. B. Reuring, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132, (2004), 1435–1443]      

A Note on Circular Decomposable Metrics

A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering of points of X, such that d(y, u) + d(z, v) d(y, z) + d(u, v) for all crossing pairs yu and zv of . We prove that any Kalmanson metric d is an l₁-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition of d can be selected to form a circular system of splits in the sense of Bandelt and Dress.     

TVS-锥度量空间中的统计收敛

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.     

On Metric Boundedness Structures

Many years ago, S.-T. Hu gave necessary and sufficient conditions for a family of subsets of a metrizable space X to be the family of bounded sets for some admissible metric for the space. In this article, we show that in any noncompact metrizable space there are uncountably many distinct metric boundedness structures. Also, given an initial metric d for X, we look carefully at the problem of characterizing those boundedness structures determined by metrics uniformly equivalent to d. Applications to hyperspaces are given. Throughout, we rely on a dual approach to the study of metric boundedness.     

ON THE LEAST DOMINANT CONTINUOUS MODULUS AND ITS APPLICATION

o.IntroductionInthispaperwedealwithqualltitativeKorovkintypetheoremsfortheaPproalmationbyboundedlinearoperatorsdefinedonC(X),andinparticularbypositiveones.HereC(X)=CR(X,d)denotestheBanachlatticeofreal-valuedcontinuousfunctionsdefinedonthecompactmetricspace(X,d)withnormgivenbylIfIlx=ma-xlf(x)I,xEX.WealsoassumethatXhasdiameterd(X)>o.ThefirstsuchtheoremforgeneralpositivelinearoperatorsandX=[a,b]equippedwiththeeuclidiandistanceisduetoR.Mamedovl4].Forspaces(X,d)beingmetricallyconvexinthes…     

Weakly conformal Finsler geometry

An extension of conformal equivalence for Finsler metrics is introduced and called weakly conformal equivalence and is used to define the weakly conformal transformations. The conformal Lichnerowicz‐Obata conjecture is refined to weakly conformal Finsler geometry. It is proved that: If X is a weakly conformal complete vector field on a connected Finsler space (M, F) of dimension , then, at least one of the following statements holds: (a) There exists a Finsler metric F₁ weakly conformally equivalent to F such that X is a Killing vector field of the Finsler metric, (b) M is diffeomorphic to the sphere and the Finsler metric is weakly conformally equivalent to the standard Riemannian metric on , and (c) M is diffeomorphic to the Euclidean space and the Finsler metric F is weakly conformally equivalent to a Minkowski metric on . The considerations invite further dynamics on Finsler manifolds.     

完备可分度量群上的齐次Levy过程的复合Poisson逼近

该文利用算子半群的方法给出了取值于具有左不变度量的完备可分群的齐次Levy过程是复合Poisson过程的弱极限这一结论．     

Banach空间中度量广义逆的乘积扰动

设X,Y为自反严格凸Banach空间.记A∈B(X,Y)为具有闭值域R(A)的有界线性算子,有界线性算子T=EAF∈B(X,Y)为A的乘积扰动.本文研究了有界线性算子A的Moore-Penrose度量广义逆的乘积扰动.在值域R(A)为α阶一致强唯一和零空间N(A)为β阶一致强唯一的条件下.给出了‖T~M-A~M‖的上界估计,作为应用,我们在L~p空间上讨论了Moore-Penrose度量广义逆的乘积扰动.     

关于Fuzzy度量空间的一点注记

本文讨论了Ｆｕｚｚｙ度量空间（Ｘ，ｄ，Ｌ，Ｋ）中几种常用的Ｋ之间的关系及其具有的相应的度量性质。     

集值动力系统中的混合性和混沌

设(X,d)是紧致度量空间.设(K,H)是X中所有非空紧子集所组成的空间,并赋予由d导出的Hausdorff度量H.主要探讨了拓扑动力系统(X,G)的混合性、混沌和集值动力系统(K,G)的混合性、混沌之间的关系,其中G是拓扑群.     

A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself. Supported by University of Palermo.     

On visual distances in density estimation: the Hausdorff choice

We consider a “visual” metric between multivariate densities that is defined in terms of the Hausdorff distance between their hypographs. This distance has been first proposed and analyzed by Beer (1982) in the non-probabilistic context of approximation theory. We suggest the use of this distance in density estimation as a weaker, more flexible alternative to the supremum metric: it also has a direct visual interpretation but does not require very restrictive continuity assumptions. A further Hausdorff-based distance is also proposed and analyzed. We obtain consistency results, and a convergence rate, for the usual kernel density estimators with respect to these metrics provided that the underlying density is not too discontinuous. These results can be seen as a partial extension to the “qualitative smoothing” setup (see Marron and Tsybakov, 1995) of the classical analogous theorems with respect to the supremum metric.     

具有（α，β）度量的复Finsler流形

设M是复流形,具有复（α,β）度量F=αφ（｜β｜/α）,其中α为M上的Hermite度量,β为M上的（1,0）形式。本文得到与F相联系的复非线性联络系数Гiμ^i的表达式,且证明了：若β为M上的全纯（1,0）形式,并且关于α的Hermite联络γij^k（z）平行,则F是M上的复Berwald度量;若α是M上的Kaihler度量,则F是M上的强Kahler Finsler度量．     

（0,2）型张量场诱导的线性变换的显表达式提取方法

对于黎曼流形（M,g）上（0,2）型光滑张量场R诱导出的线性变换R＊：X（M）→X（M）,其隐表达式为g（R＊（X）,Y）=S（X,Y）,X,Y∈X（M）,研究了从局部上提取出R＊（X）的显表达式的方法.提出一种所谓g正定提取方法,并将这种方法进一步应用到度量保形变换下的线性变换Φ＊（X）,L＊（X）.     

Banach空间中一类集值度量广义逆的连续线性选择

对于Banach空间中余一维闭值域有界线性算子的集值度量广义逆,给出其具有连续线性选择的充分必要条件.结果是对M.Z.Nashed与G.F.Votruba提出的研究问题的部分回答.     

Banach空间中线性算子方程的约束极值解

设X,Y与Z为Banach空间L∈L(X,Z),T∈L(X,Y)为线性算子.运用线性算子的度量广义逆概念,在L(x)=y的极值解集合中,给出T(x)=h的约束极值解的精确刻画.     

A new weighted metric: the relative metric II

In the first part of this investigation we generalized a weighted distance function of R.-C. Li's and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries and quasiconvexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.     

Hutchison度量完备的充要条件

距离空间Ｘ上，以Ｍ（Ｘ）记定义在Ｘ的Ｂｏｒｅｌ域上的具有有界支撑的概度测度全体，Ｒ（Ｘ）记Ｍ（Ｘ）中所有Ｒａｄｏｎ测度，Ｍ（Ｘ），Ｒ（Ｘ）均赋予Ｈｕｔｃｈｉｓｏｎ度量，本文得到：Ｒ（Ｘ）完备当且仅当Ｘ完备且有界，若Ｘ可分，则：Ｍ（Ｘ）完备当且仅当Ｘ完备且有界。     

Banach空间中线性流形上的度量投影的表达式

借助于正规对偶映射,建立了一般Banach空间中线性流形上的(集值)度量投影存在的 充要条件,同时给出了度量投影的表达式和点到线性流形上的距离公式.这些本质地推广和改进了 王玉文和于金凤在空间自反、严格凸和光滑强假定下的相应结果.