First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit rela...First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.展开更多
Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying...Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.展开更多
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operat...In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.展开更多
Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function betw...Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.展开更多
A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several k...A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.展开更多
In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of xed points by using some necessary conditions. The results directly improve and gene...In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of xed points by using some necessary conditions. The results directly improve and generalize some xed point results in metric spaces and some previous results in cone metric spaces.展开更多
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac...In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.展开更多
The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
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 nite intersection property and...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 nite intersection property and which for every c ∈ E; 0 《 c contains a set of diameter less that c has non-empty intersection.展开更多
In this short note, we consider the perturbation of compact quantum metric spaces. We first show that for two compact quantum metric spaces （A, P） and （B, Q） for which A and B are subspaces of an order-unit space ...In this short note, we consider the perturbation of compact quantum metric spaces. We first show that for two compact quantum metric spaces （A, P） and （B, Q） for which A and B are subspaces of an order-unit space t and P and Q are Lip-norms on A and B respectively, the quantum Gromov-Hausdorff distance between （A, P） and （B, Q） is small under certain conditions. Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given.展开更多
令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作...令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作为证明的一个应用,本文也刻m画了算子S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i)的类似性质.展开更多
In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some...In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).展开更多
文摘First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.
基金supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)
文摘Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.
文摘In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.
文摘Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.
基金Supported by National Natural Science Foundation of China(Grant No.11801177)Postdoctoral Science Foundation of China(Grant No.2020M671471)Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.
基金Supported by the Graduate Initial Fund of Hubei Normal University(2008D36)Supported by the Foundation of Education Ministry of Hubei Province(D20102502)
文摘In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of xed points by using some necessary conditions. The results directly improve and generalize some xed point results in metric spaces and some previous results in cone metric spaces.
文摘In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
文摘The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
基金Foundation item： Supported by tile National Natural Science Foundation of China（10971185, 10971186） Supported by the Research Fund for Higher Education of Fujian Province（JK2011031）
文摘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 nite intersection property and which for every c ∈ E; 0 《 c contains a set of diameter less that c has non-empty intersection.
文摘In this short note, we consider the perturbation of compact quantum metric spaces. We first show that for two compact quantum metric spaces （A, P） and （B, Q） for which A and B are subspaces of an order-unit space t and P and Q are Lip-norms on A and B respectively, the quantum Gromov-Hausdorff distance between （A, P） and （B, Q） is small under certain conditions. Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given.
文摘令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作为证明的一个应用,本文也刻m画了算子S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i)的类似性质.
基金supported by National Natural Science Foundation of China(Grant Nos.11401425,11626134,11701300,11671212 and 51535008)K.C.Wong Magna Fund in Ningbo University。
文摘In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).
