Banach空间中增生算子方程的Ishikawa迭代解

在没有∑∞n=0αnβn<∞的更弱条件下,使用与完全不同的方法,证明了Ishikawa迭代序列强收敛Lipschitz连续的增生算子T的方程x+Tx=f的唯一解,并提供了更为全面和一般的收敛率的估计.本文结果是引文[3-4]中相应结果的统一和发展.     

Some remarks on a game of Telgársky

In [3] R. Telgársky (1975) asked: does the first player have a winning strategy in the game G(F,X×X) if the first player has a winning strategy in the game G(F,X)? I give a positive answer to this question and prove that this result is also true for spaces where the first player has a winning strategy in game G(K,X) where K=1, F, C, for σC if X is P-space and for DC if X is collectionwise-normal space. The last result is related to the Telgársky's (1983) conjecture discussed in [1]. These results are not true for infinite product of spaces.     

Convergence Theorems for Non-Self Mappings in CAT(0) Spaces

In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △? convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature.     

Sobolev estimates for optimal transport maps on Gaussian spaces

In this work, we will take the standard Gaussian measure as the reference measure and study the variation of optimal transport maps in Sobolev spaces with respect to it; as a by-product, an inequality which gives a precise link between the variation of entropy, Fisher information between source and target measures, with the Sobolev norm of the optimal transport map will be given. As applications, we will construct strong solutions to Monge–Ampère equations in finite dimension, as well as on the Wiener space, when the target measure satisfies the strong log-concavity condition. A result on the regularity on the optimal transport map on the Wiener space will be obtained.     

椭球约束下误差方差非负二次估计的可容许性

本文给出了线性模型中椭球约束下，误差方差非负二次估计可容许的一个必要条件，并且，对于线性模型中设计阵X＝1nj=(1,1,…，1）′的特殊情形，本文给出了一个充要条件。     

Singular Measures and (1,p)-Capacity on Weighted Sobolev Classes

Conditions are studied under which the contribution of the singular part of a measure to the (1,p)-capacity of an arbitrary condenser is zero.     

闭极大线性子空间正交补的判别及应用

继续前面的工作,证得对于赋范线性空间中固定线性子空间成为迫近子空间的充分必要条件.特别的,对于闭极大线性子空间来说,的迫近性等价于的正交可补性.做为其直接推论,给出Banach空间成为自反空间的5个等价条件,其中4个条件为经典结果,一个条件为已有文献中给出的条件,但给出全新的证明.     

物价、利率与收入对居民消费需求影响研究——基于时变参数状态空间模型

运用时变参数状态空间模型对我国改革开放三十年来物价、利率与收入对农村和城镇居民消费需求影响的动态特征进行了研究。发现物价、收入对农村和城镇居民的消费需求弹性不同,农村消费需求受收入影响较大,而城市居民消费需求受物价影响较大;利率对农村和城镇居民消费需求影响不显著,利率机制目前还不是调解中国消费需求的理想工具。在此基础上给出了相应的政策建议。     

Exceptional family of elements for general order complementarity problems

The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements. Finite dimensional examples and an application to integral operators will be given.     

MULTILINEAR CALDER(O)N-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderón-Zygmund operator can be obtained.