THE UNIT BALL OF C*-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

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＂.     

THEORY OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS IN COMPLEX DOMAIN

In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.     

非扩张映射的不动点与变分包含问题的公共解

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inclusion for an inverse-strongly monotone mapping and a maximal monotone mapping in a real Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using the result, we consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space.     

ON THE INTERIOR REGULARITIES OF THE SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

In we discussed the problems of calculus of variations with strong nonlinearity. Its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficients,We get the interior regularities of the solutions of(1). It is just the Hilbert's 19th problem in the case with strong nonlinearity.     

DISTORTION ESTIMATES OF SYMMETRIC POINTS OF QUASICIRCLE

Let ξ=f(z) be a K-quasiconformal mapping (K-Q.C.) in the complex plane, f(∞)=∞. The image of the real axis under ξ=f(z) is a quasicirclz and the points ξ=f(z) and ξ=f(z) are a pair of symmetric points of the circle, we know that the connection between the quasicircle and the quasiconformal extention is essential. The distortion estimates of the quasicircle and of the symmetric points are both interesting. It is known that there exist two constants C_1(K) and C_2(K), depending on K oniy, such that the inequality     

2一致凸Banach空间中均衡问题、变分不等式问题和不动点问题的一个弱收敛定理

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.     

ESTIMATION OF SPATIAL AR MODELS

In this paper,some results in [1] on parameter estimation of spatial AR models are improved.Moreover,using some recent results on convergence rate of sample autocorrelations,we give strongly consistent order estimates for spatial AR models and iterated logarithmic convergence rate for AR parameter estimates, which improve the result in [2] of weakly consistent order estimation and strongly consistent parameter estimation.     

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson's extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson's extrapolation.     

THE UNIQUENESS OF LIMIT CYCLE AND CRITICAL POINT FOR A CLASS OF CUBIC SYSTEM

In this paper,we consider an accompany system concerning some class of cubic system. We then prove that the system has at most one limit cycle. Finally,we obtain the topological structure of both the critical points at infinity and the singular points lying on invariant lines.     

Strongly exposed points, Helson-Szegö weights and Toeplitz operators

We investigate the strongly exposed points of the unit ball ofH ¹ and show that these functions are characterized by the equality of two De Branges' spaces that appeared in earlier results on exposed points. It then follows that the strongly exposed points are induced by Helson-Szegö weights, leading to several interesting properties of this class of functions.Dedicated to my father, Albert Jan Beneker.     

On exposed functions in Bernstein spaces

For σ > 0, the Bernstein space {ie427-01} consists of those L ¹(ℝ) functions whose Fourier transforms are supported by [−σ, σ]. Since {ie427-02} is separable and dual to some Banach space, the closed unit ball {ie427-03} of {ie427-04} has sufficiently large sets of both exposed and strongly exposed points: {ie427-05} coincides with the closed convex hull of its strongly exposed points. We investigate some properties of exposed points, construct several examples, and obtain as corollaries relations between the sets of exposed, strongly exposed, weak* exposed, and weak* strongly exposed points of {ie427-06}.     

Exposedness in Hardy spaces of domains of finite connectivity

In this paper we investigate various properties of (strongly) exposed points in the unit ball of the Hardy sapce H¹ over a domain of finite connectivity, and discuss how these compare with results for the units disc.     

Dentability and extreme points in Banach spaces

It is shown that a Banach space E has the Radon-Nikodym property (equivalently, every bounded subset of E is dentable) if and only if every bounded closed convex subset of E is the closed convex hull of its strongly exposed points. Using recent work of Namioka, some analogous results are obtained concerning weak¹ strongly exposed points of weak¹ compact convex subsets of certain dual Banach spaces.     

Strongly Exposed Points in the Ball of the Bergman Space

We investigate which boundary points in the closed unit ball of the Bergman space A¹ are strongly exposed. This requires study of the Bergman projection and its kernel, the annihilator of Bergman space. We show that all polynomials in the boundary of the unit ball are strongly exposed.     

Orlicz型序列空间的暴露性

对赋Luxember范数或Orlicz范数的Orlicz型序列空间,诸如古典的、广义的及参数式的,本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画,并对以往结果中的错误进行了修正,从而在序列空间方面系统地完成了有关暴露性的刻画。     

Null Sequences in Coechelon Spaces

Rotundity of finite -dimensional Orlicz spaces l^?_n equipped with the Luxemburg norm is considered. It is proved that criteria for rotundity of l^?_nfor n ≥ 3 does not depend on n and are the same as the criteria for rotundity of the inhite-dimensional subspace h^? of an Orlicz sequence spacel^?. Criteria for rotundity of l^?₂ are different. Next, criteria for exposed points, (H)- points, strongly exposed points and LUR- points of the unit sphere of l^? and of its subspace h^? are given.     

Strongly exposed points in uniform algebras

In this paper we show that the unit ball of an infinite dimensional function algebra has no strongly exposed points.

     

Exposed and Strongly Exposed Points of Finite Order in Some Banach Spaces

in this paper we study the exposed and strongly exposed points of finite order inl(D,X) as well as in L(ll (D,X), Y) and L(X, l(D,Y) ), where X and Y are real Banachspaces while D is a non empty index set. In particular, we characterize the exposed andstrongly exposed points in these spaces.