关于度量投影的连续性

本文引入的Ｂａｎａｃｈ空间的（Ｃ－Ｉ）、（Ｃ－Ⅱ），（Ｃ－Ⅲ）等几何性质，证明了如下结果。设Ｍ是Ｂａｎａｃｈ空间的逼近凸子集，如果Ｂａｎａｃｈ空间有性质（Ｃ－Ｉ），（Ｃ－Ⅱ）（Ｃ－Ⅲ），则度量投影ＰＭ连续（范数－范数上半连续，范数－弱上半连续）。这些结果推广了文（４，７，８）相应的定理。最近，Ｄ．Ｋｕｔｚａｒｏｖａ，Ｂｏｒ－Ｌｕｈ Ｌｉｎ等引入了一些新的凸性空间，本文还研究了这些凸性空间中度量投影     

B值拟终鞅型序列与Banach空间的几何特征

设（Ω，，Ｐ）是概率空间，Ｂ是Ｂａｎａｃｈ空间．本文引入了一类新的鞅型序列──（Ｂ值）拟终鞅型序列，并研究了它们的收敛性与Ｂａｎａｃｈ空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性，一致光滑性和ＵＭＤ性的依赖关系．     

有限元的一个局部超收敛结果

１．引 言 设 是一个有界开域，具充分光滑的边界 且设 是 上的一族拟一致的三角剖分，用 表示定义在Ｔｈ上的分片线性有限元空间，并置考虑模型问题 用 分别表示的有限元解及内插，那么有插值估计：（见［１］）一般地，如ｕ为问题（１．１）的解，我们有有限元逼近误差估计（见［３］） 命题１．设 并设 分别表示按定义的Ｇｒｅｅｎ函数及其有限元逼近，那么有其中 Ｃ与 ｚ，ｈ无关．（参见［３］） 注意．如 且 ，那么至少存在一个点 ，使即ｘ０是ｆ的奇点，例如其中 为常数， ，显然如果。，如果故我们假定 本文将证明，误差与ｆ的奇性…     

关于Poincaré度量与Bers逼近定理

本文首先给出区域Ｄ的Ｐｏｉｎｃａｒé度量λ（ｚ）的几个有关性质，然后推广Ｂｅｒｓ逼近定理，得到主要结果如下：设Ｄ是连通数为有穷的有界区域，记Ａｑ（Ｄ）为Ｄ内满足｜｜ｐ｜｜＝∫∫＿Ｄ［λ（ｚ）￣（２－９）｜ψ（ｚ）｜｜ｄｚ∧ｄｚ＜∞的解析函数ψ之全体构成的Ｂａｎａｃｈ空间（其中整数ｑ≥２），Ｒｑ（Ｄ，Ｔ）（ＴＣ（ｃ－Ｄ））表示Ａｑ（Ｄ）中极点在Ｔ的有理函数子空间，当Ｔ满足Ｂｅｒｓ逼近定理条件时，Ｒｑ（Ｄ，Ｔ）在Ａｑ（Ｄ）中稠密。     

Banach空间中微分方程的弱Caratheodory解

本文在一般Ｂａｎａｃｈ空间中讨论微分方程的初值问题；ｕ’＝ｆ（ｔ，ｕ），ｕ（０）＝ｘ０。设ｆ（ｔ，ｕ）不连续，仅满足所谓弱Ｃａｒａｔｈｅｏｄｏｒｙ条件，但仍证明了初值问题的解可由迭代序列的一致极限得到，并给出了逼近解的迭代序列的误差估计。对周期边值问题得到了类似的结果。     

某些周期卷积类上的最佳单边逼近

设Ｋ满足性质Ｂ（或Ｋ是ＮＣＶＤ核），本文得到了以Ｋ为核的卷积类Ｂ＿ｐ（或Ｋ＿ｐ），１≤ｐ≤∞，在Ｌ＿１尺度下，借助于三角多项式和周期样条的单边逼近的精确值．ｈ，ｆ⊥Ｓ，则ｈ⊥Ｓ，结合（４．７）我们易知Ｆ∈Ｓ￣－（Ｇ￣＊），且Ｆ⊥Ｓ，Ｆ（０）＝０．由引理６得由引理７得进一步地根据定理２，我们可得（４．６）及（４．８）得另一方面．根据［２］（定理１．７．５）及引理８得由（４．８）、（４．１０）定理得证．作者感谢导师孙永生教授的悉心指导．参考文献     

双特征的Beltrami方程和拟正则映射

设Ω为Ｒｎ上的一个区域，ｎ２，对于具有双特征矩阵Ｇ（ｘ），Ｈ（ｘ）∈Ｃｋ，α（Ω，Ｒｎ），ｋ１，０＜α＜１的Ｂｅｌｔｒａｍｉ方程（１．４），建立了在Ｓｏｂｏｌｅｖ空间Ｗ１，ｎｌｏｃ（Ω，Ｒｎ）上广义解的正则性：ｆ（ｘ）∈Ｃｋ＋１，δｌｏｃ（Ω），对某一δ：０＜δ＜１．     

渐近非扩张型的自映象族的不动点与几乎轨道的渐近行为

设Ｃ是一致凸Ｂａｎａｃｈ空间Ｅ的非空闭凸子集,Г＝｛Ｔｔ：ｔ ∈ Ｓ｝是Ｃ上渐进非扩张型的自映象族,使得对每个ｔ∈Ｓ,Ｔｔ：Ｃ→Ｃ连续,其中,Ｓ是有单位元的交换的拓扑半群．又设｛ｕ（ｔ）：ｔ∈Ｓ｝是Г的几乎轨道．本文证明了,若Г在｛ｕ（ｔ）：ｔ∈ Ｓ｝关于Ｃ的渐近中心ｃ∈Ｃ处渐近正则,则下列叙述等价：（ｉ）Ｔｔ,ｔ∈Ｓ的所有公共不动点之集Ｆ（Г）非空;（ｉｉ）｛ｕ（ｔ）：ｔ∈Ｓ｝局部有界;（ｉｉｉ）ｌｉｍｔ｜｜Ｔｔｃ－ｃ｜｜＝０;（ｉｖ） ｃ∈ Ｆ（Г）．进一步,运用该结果,本文建立了渐近非扩张族的几乎轨道的渐近行为方面的结果．     

Banach空间上非Lipschitz映射的渐近行为

设Ｃ是具Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间Ｅ的非空凸闭子集，Ｇ是定向集．｛Ｔ_ｔ：ｔ∈Ｇ｝是Ｃ上的渐近非扩张型映照．本文给出了｛Ｔ_ｔ：ｔ∈Ｇ｝的弱收敛定理．     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

Best Uniform Approximation of a Family of Functions Continuous on a Compact Set

We investigate the problem of the best uniform approximation of a function continuous on a compact set. We generalize the principal results of this investigation to the problem of the best simultaneous uniform approximation of a family of functions continuous on a compact set.     

Algorithms for the Best Simultaneous Uniform Approximation of a Family of Functions Continuous on a Compact Set by a Chebyshev Subspace

We generalize the cutting-plane method and the Remez method to the case of the problem of the best simultaneous uniform approximation of a family of functions continuous on a compact set.     

一致凸度量线性空间的自反性及其应用

为研究度量线性空间中凸集的逼近性质，Ｇ．Ｃ．Ａｈｕｊａ等引起了度量线性空间的严格凸性及一致凸性的定义。本文证明了完备的一致凸的度量线性空间是自反的。同时，作为应用，研究了最佳联合逼近元的存在性与唯一性问题。     

Characterization of best uniform coapproximation

This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.     

Characterization of best uniform coapproximation

This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.     

车辆牌照拍卖模型

提出多个相同物品(如车辆牌照)同时密封拍卖的模型，给出对称均衡竞标策略；证明了该拍卖方式与第一价格密封连续拍卖产生相同的预期收益；对估价为均匀分布的拍卖预期收益进行了研究。     

UNIQUENESS OF MINIMIZATION PROBLEMS

In this paper we give a uniqueness theorem for a minimization problem.Meanwhile weprovide a uniform uniqueness theorem for L_p(1≤p≤∞)simultaneous approximationsincluding mean simultaneous approximation and Chebyshev simultaneous approximation.     

Cournot tâtonnement and dominance solvability in finite games

If a finite strategic game is strictly dominance solvable, then every simultaneous best response adjustment path, as well as every non-discriminatory individual best response improvement path, ends at a Nash equilibrium after a finite number of steps. If a game is weakly dominance solvable, then every strategy profile can be connected to a Nash equilibrium with a simultaneous best response path and with an individual best response path (if there are more than two players, switches from one best response to another may be needed). Both statements remain valid if dominance solvability in the usual sense is replaced with “BR-dominance solvability”, where a strategy can be eliminated if it is not among the best responses to anything, or if it is not indispensable for providing the best responses to all contingencies. For a two person game, some implications in the opposite direction are obtained.     

Closed convex sets and their best simultaneous approximation properties with applications

We develop a theory of best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of closed convex sets, and give necessary and sufficient conditions for the uniqueness of best simultaneous approximation. We give a characterization of simultaneous pseudo-Chebyshev and quasi-Chebyshev closed convex sets in X. Also, we present various characterizations of best simultaneous approximation of elements by closed convex sets in terms of the extremal points of the closed unit ball B _X* of X*.     

On well posedness of best simultaneous approximation problems in Banach spaces

The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.