Day范数的c0（Γ,Χ）的暴露点和光滑点

设Γ为非空集,Ｘ为实Ｂａｎａｃｈ空间,本研究赋Ｄａｙ范数的ｃ０（Γ,Ｘ）的光滑点,强光滑点,暴露点和强暴露点。     

Renormings concerning exposed points and non-smoothness

Intuitively, non-smooth points might look like exposed points. However, in this paper we show that real Banach spaces having dimension greater than or equal to three can be equivalently renormed to obtain non-smooth points which are also non-exposed.     

Properties of symmetric matrices

We find the extreme points and the smooth points of the unit ball of the Banach space n_℘ of all real symmetric (n×n)-matrices.     

THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'p

Byσthe author denotes the areal measure on the unit disk D=z: |z|<1. Let H'p={f(z): f(z) is analytic in D and 1/π∫D|f(z)|p dσ<+∞}. Let B(H＇p)={f:f∈H＇p and 1/π∫D|f(z)|p dσ1. This article researches the support points and extreme points of B(H'p).     

A short note about exposed points in real banach spaces

We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.     

Recurrent points and non-wandering points of graph maps

Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps.     

关于迭代函数不动点的研究

In this paper the following results are got 1. We prove that the order definitionwhich is given by J.F. Trawb on the iterative function is wrong. 2. A existent theorem on the repulsive point is given. 3. We give some theorems to judge a fixed point of iterative function. They all imporve the Ostrowski's theorems.     

星形函数族的一个子族的极值点与支撑点

设T={f(z):f(z)在单位圆盘|z|<1上解析,f(z)=z ,an是实数, |an|≥|an 1|且|an|≤1}．该文找出了解析函数族T的极值点与支撑点.     

On the number of triple points of an immersed surface with boundary

Given a generic immersionf:S ¹→S ² of a circle into the sphere, we find the best possible lower estimation for the number of triple points of a generic immersionF: (M, S ¹)→(B ³,S ²) extendingf, whereM is an oriented surface with boundary ∂M=S ¹,B ³ is the 3-dimensional ball with boundaryS ². Supported by the Hungarian National Science and Research Foundation OTKA 2505 Supported by the Hungarian National Science and Research Foundation OTKA T4232 This article was processed by the author using the Springer-Verlag T_EX P Jour1g macro package 1991.     

Extreme points, exposed points, differentiability points in CL-spaces

This paper presents a property of geometric and topological nature of Gateaux differentiability points and Fréchet differentiability points of almost CL-spaces. More precisely, if we denote by a maximal convex set of the unit sphere of a CL-space , and by the cone generated by , then all Gateaux differentiability points of are just n-s, and all Fréchet differentiability points of are (where n-s denotes the non-support points set of ).

     

Polynomials hardly commuting with increasing bijections

Let I be an interval in the real line ℝ. Among the real polynomials that take I to I, we ask which ones do not commute with any increasing bijection of I other than identity. For this purely algebraic problem, the solution involves concepts in topological dynamics. Our main characterizations are in terms of full orbits of critical points and periodic points. Using these, we obtain simpler criterion, namely, that for no nontrivial subinterval K⊂I, the successive images {f ⁿ (K):n=0,1,2,…} form a pairwise disjoint collection. This problem is of interest in topological dynamics because it is about characterization of polynomials with unique self-topological-conjugacy.     

某些Banach空间的有限阶光滑点和强光滑点（英）

本文给出l_∞(X)以及L(l₁(X),Y),L(X,l_∞(Y))和L(X,c₀(Y))的单位球的有限阶光滑点和强光滑点的充要条件，这里X和Y都是任意的Banach空间.特别地，本文给出这些空间的单位球的光滑点和强光滑点的充要条件.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

Best proximity point theorems for single- and set-valued non-self mappings

We study the existence of best proximity points for single-valued non-self mappings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.     

Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel

In this paper we establish an existence of solution theorem and an existence of bifurcation point theorem for Hammerstein integral equation whose kernel is supposed neither symmetric nor positive defined. To prove our result, we use the Tychonoff fixed point theorem. In particular, our bifurcation result is directly comparable with an analogous one recently established by F. Faraci.     

单位圆内代数体函数的Borel点和Nevanlinna点

本文对单位圆内的代数体函数 w(z)定义了 Borel 点和 Nevanlinna 点,证明了 Nevanlinna 点的存在性,并在 w(z)的级为有穷时,亦证明了 Borel 点的存在性。     

Repelling periodic points of given periods of rational functions

Let R(z) be a rational function of degree d≥2. Then R(z) has at least one repelling periodic point of given period k≥2, unless k = 4 and d = 2, or k = 3 and d≤3, or k = 2 and d≤8. Examples show that all exceptional cases occur.     

“关于曲线拐点判别法”一文中若干问题的理论分析

对文于淑兰提出的判别曲线拐点的两个定理及推论作了充分的研究,指出了定理证明的错误原因,并且否定了其中的一个定理及其推论.     

重心坐标系下平面上三次Bézier曲线奇拐点的分布

本文利用重心坐标,研究Bzier曲线奇拐点的分布,绘出了奇拐点存在的区域和充要条件,简化了判别Bzier曲线奇拐点的充要条件,并给出了Bzier曲线的重心坐标表示方法.     

《微积分中值定理间点的关系》注记

微分中值定理的结论是在开区间内至少存在一点使得某个等式成立,不妨把这样的点称为微分点;积分中值定理的结论也是在开区间内至少存在一点使得某个等式成立,不妨把这样的点称为积分点.本文讨论这两类点之间是否有关系,以及关系如何的问题,指出相关文献所提供的若干个结论中,有不只一个存在错误.