集合的距离与最近点对的性质

本文研究不相交二集Ｆ，Ｇ的最近距离ρ（Ｆ，Ｇ）＝ｉｎｆｘ∈Ｆ，ｙ∈Ｇρ（ｘ，ｙ），当存在最近点对（ｘ０，ｙ０），即ρ（ｘ０，ｙ０）＝ρ（Ｆ，Ｇ），这对点（ｘ０，ｙ０）何时唯一及非唯一时性态如何。Ｆ，Ｇ主要设为超平面、直线、凸集或严凸集。严凸集保证了唯一性。超平面则对非唯一性影响较大。文章又建立了一些带距离性的分离定理。     

一类非线性积分方程正解的存在唯一性

本文研究积分方程ｕ（ｘ）＝λ∫_Ωｋ（ｘ，ｙ）ｆ（ｙ，ｕ（ｙ））ｄｙ，λ＞０及其它的非线性摄动ｕ（ｘ）＝λ∫_Ωｋ（ｘ，ｙ）ｆ（ｙ，ｕ（ｙ））ｄｙ＋Ｇ（ｕ（ｘ）），在ｋ（ｘ，ｙ）非负可测，ｆ（ｘ，ｕ），Ｇ（ｕ）满足一定条件下，得到所述方程解的存在唯一性及其迭代逼近．     

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．     

点 直线 平面之间的对称性的解析表达式

点直线平面之间的对称性的解析表达式艾则孜·卡得尔（新疆和田高等师专数学系８４８０００）命题１Ｐ１（ｘ１，ｙ１，ｚ１）关于Ｐ０（ｘ０，ｙ０，ｚ０）点的对称点的坐标为：命题２平面Ａｘ＋Ｂｙ＋Ｃｚ＋Ｄ＝０外一点Ｐ０（ｘ０，ｙ０，ｚ０）关于该平面的对称点的坐...     

矩阵的Γ逆在一类约束系统中的应用

将矩阵的Γ逆应用于约束系统Ａｘ＋ｙ＝ｂ，ｘ∈Ｌ，ｙ∈Ｌ^⊥，对任意的Ａ和Ｌ，表示了它的一般解。当ＡＰ_Ｌ＋Ｐ_Ｌ⊥可逆时，这个解正是Ｂｏｔｔ—Ｄｕｆｆｉｎ解。并就Ｌ是Ａ的约化子空间、不变子空间及一般情形，讨论了相应的Γ逆存在的条件。     

二次曲线定比分点弦的存在定理

文 [1 ][2 ]分别给出了求二次曲线定比分点弦所在直线方程的消去法和较为简洁的解方程方法 ,本文就二次曲线定比分点弦存在区域作一探讨 ,以使这类问题进一步完善 .设定 :Ｆ(ｘ ,ｙ) =Ａｘ2 +2Ｂｘｙ+Ｃｙ2 +2Ｄｘ+2Ｅｙ+Ｆ ,　φ(ｘ,ｙ) =Ａｘ2 +2Ｂｘｙ+Ｃｙ2 ,ｆ1 (ｘ,ｙ)=Ａｘ+Ｂｙ +Ｄ ,　ｆ2 (ｘ ,ｙ) =Ｂｘ+Ｃｙ +Ｅ ,Ｉ2 =Ａ　ＢＢ　Ｃ ,Ｉ3=Ａ　Ｂ　ＤＢ　Ｃ　ＥＤ　Ｅ　Ｆ.定理　过Ｐ(ｘ0 ,ｙ0 )的直线交二次曲线Ｆ(ｘ ,ｙ) =0于Ｐ1 、Ｐ2 两点 ,点Ｐ分Ｐ1 Ｐ2 的比为λ ,则Ｐ(ｘ0 ,ｙ0 )满足　Ｆ(ｘ0 ,ｙ0 ) Ｉ2 Ｆ(ｘ0 ,ｙ0 ) -…     

在奇次Legendre多项式零点上的（0，2）*插值

设Ｐ_ｎ表示ｎ次Ｌｅｓｅｎｄｒｅ多项式，本文考虑多项式（１－ｘ²）Ｐ_ｎ．（ｘ）／ｘ（ｎ为奇数）零点上的（０，２）^*插值问题，得到了这种插值的正则性，显式表达式及收敛性．     

有序Banach空间中一类算子方程的正解

本文考虑有序Ｂａｎａｃｈ空间中形如：ｘ＝ｙ＋Ｋｆ（·，Ｐ_１ｘ，…，Ｐ_ｎｘ）的算子方程，利用一定的不动点定理，得到了这类方程存在正解的某些充分条件。     

Dirac定理的局部化与Hamilton图

设Ｇ为一个ｎ阶２－连通图，ｎ≥３．若｜Ｄ_ｎ／２（Ｋ_１，３）｜≥２且满足下述条件之一：ｉ）｜Ｄ_ｎ／２（Ｋ_１，３＋ｅ）｜≥２，ii）若Ｋ_１，３＋ｅ→Ｇ，ｘｙ(?)Ｅ（Ｋ_１，３＋ｅ），则ｍａｘ｛ｄＧ（ｘ），ｄＧ（ｙ）｝≥ｎ／２，则Ｇ是一个Ｈａｍｉｌｔｏｎｉａｎ图或其闭包为ｓＰ|⊕Ｈ，这里ｓＰ⊕Ｈ是一类极小２－边连通图．     

共振情形下次线性椭圆偏微分方程的解

研究了共振下的微分方程Δｕ＋λ_１ｕ＋ｇ（ｘ，ｕ）＝０，ｘ∈?Ω；ｕ｜_?Ω＝０．在ｇ（ｘ，ｕ）关于ｕ次线性的情形，证明了解的存在性，从而部分地回答了Ｆｉｇｕｅｉｒｅｄｏ ａｎｄ Ｍａｓｓａｂｉ的一个问题．     

A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions

We introduce a notion of pointwise cyclic contraction T satisfying TA ? B and TB ? A to obtain the existence of a point x ∈ A, such that d(x, Tx) = dist(A, B), known as a best proximity point for such a map. We also prove that for any x ∈ A, the Picard iteration {T²ⁿx} converges to a best proximity point.     

Optimum solutions for a system of differential equations via measure of noncompactness

New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations.     

Extensions of Edelstein's Theorem on Contractive Mappings

The aim of this article is to provide extensions of Edelstein's theorem for a class of contractive mappings, namely cyclic contractive mappings. We prove the existence and convergence of best proximity points of a cyclic contractive map. We also discuss continuity properties of cyclic contractive maps. Finally, we give a characterization of such maps in the setting of a Hilbert space.     

Best Proximity Pair Results for Relatively Nonexpansive Mappings in Geodesic Spaces

Given A and B two nonempty subsets in a metric space, a mapping T: A ∪ B → A ∪ B is relatively nonexpansive if d(Tx, Ty) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, Tx) = dist(A, B). In this work, we extend the results given in Eldred et al. (2005) [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, 283–293] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in A × B of a pair of best proximity points.     

On Bregman Best Proximity Points in Banach Spaces

In this article, using Bregman functions and Bregman distances, we first introduce the notion of Bregman best proximity points, extending the notion of best proximity points introduced and studied in [1 K. Fan (1969). Extensions of two mixed point theorems of F. E. Browder. Math. Z. 122:234–240.[Crossref], [Web of Science ®] , [Google Scholar]]. We then prove existence and convergence results of Bregman best proximity points for Bregman cyclic contraction mappings in the setting of Banach spaces. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. Numerical examples are included at the end of the paper. So, our results improve and generalize many known results in the current literature.     

Tor-torsion pair与弱整体维数

利用torsion pair的方法讨论了Tor-torsion pair的一些性质,目的是找到Tor—torsion pair与环局的弱整体维数之间的关系,并得到了一个很好的不等式关系．     

Subweakly Biased Pairs and Jungck Contractions with Applications

The existence of common fixed point results for a weakly biased pair under Jungck contraction is established. We define a new class of subweakly biased pair which properly contains the classes of C _q -commuting, pointwise R-subweakly commuting and R-subweakly commuting maps and establish common fixed point results for this class of maps. As applications several invariant best approximation results are proved which unify, extend, and complement the well-known results.     

Best proximity pair theorem in metrizable topological vector spaces

The object of this paper is to prove an existence result on best proximity pair. For this purpose, the class of factorizable multifunctions in approximately weakly compact, convex subset of metrizable topological vector space is used. As consequence, our theorem generalizes the result of Basha and Veeramani^[10]. Finally, certain known results have also been obtained as corollaries in this work.     

函数空间的邻近及其收敛性

本文首先研究了函数空间的点态收敛的邻近结构,其次给出了函数空间一致收敛的邻近结构并研究了使之成为联合邻近连续的条件;最后研究了函数空间在子集族上一致收敛的邻近及其性质