THE MODULUS OF CONVEXITY AND THE EQUIVALENT CONDITIONS OF UNIFORMLY NON-SQUARE SPACES

This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.

ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE

In this article, the authors study a generalized modulus of convexity, δ（α） （ε）. Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^（α）（1＋ε ） 〉 （1- α）ε.

NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES

The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.

A New Class of Banach Spaces with Uniform Normal Structure

Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.

Various Expressions for Modulus of Random Convexity

We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0（F, X） derived from a normed space X by the classical modulus of convexity of X.

FUNCTION OF CONVEXITY AND REFLEXIVITY

Let X be normed linear space, 8 (X)={x∈X|‖x‖ = 1}. The author tried to introduce the concept of the function of convexity for any BANACH space, as J. A. Clarkson had introduced the concept of modulus of convexity for uniformly convex space.

A REMARK ON CERTAIN DIFFERENTIAL INEQUALITIES INVOLVING p-VALENT FUNCTIONS

In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.

Lipschitz-continuity of Spherically Convex Functions

In this article,some basic and important properties of spherically convex functions,such as the Lipschitz-continuity,are investigated.It is shown that,under a weaker condition,every family of spherically convex functions is equi-Lipschitzian on each closed spherically convex subset contained in the relative interior of their common domain,and from which a powerful result is derived:the pointwise convergence of a sequence of spherically convex functions implies its uniform convergence on each closed spherically convex subset contained in the relative interior of their common domain.

相关于增长函数的非交换Orlicz空间的一致凸性

相关于增长函数的非交换Orlicz空间是拟Banach空间,研究了这类拟Banach空间的一致凸性.首先,得到了这类空间上的模和Luxemburg拟范数的控制关系.其次,给出了这类空间的一致凸性,并且估计了凸性的模.最后,给出了满足假设的具体空间的例子.

An L^0(F,R)-valued Function's Intermediate Value Theorem and Its Applications to Random Uniform Convexity

Let （Ω, F, P） be a probability space and L0（F,R） the algebra of equivalence classes of real- valued random variables on （Ω, F, P）. When L0（F,R） is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0（F, R） to L0（F,R）. As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module （S, ｜｜·｜｜） is random uniformly convex iff LP（S） is uniformly convex for each fixed positive number p such that 1 〈 p 〈 ＋∞.

广义凸性模在不动点中的应用

通过对广义凸性模与弱正交系数关系的研究,得到了Banach空间具有一致正规结构的充分条件,从而得到了Banach空间上的单值非扩张映射存在不动点的充分条件,并且证明了上述条件同样使得Banach空间上的集值非扩张映射也存在不动点。

Banach空间的凸性模与正规结构(英文)

令X是Banach空间,根据凸性U-模与凸性W*-模和弱正交系数之间的关系来证明Banach空间X具有正规结构.由此加强了一些已知的结论.

Banach空间的凸性模与光滑模

定义了TC凸性模,TC光滑模,刻划了一致凸性与一致光滑性,并研究了取值于Banach空间的特殊鞅不等式与一致凸性,一致光滑性的关系.

函数的最凸点与一致可导性

给出了函数的最凸点的定义,刻画了几类基本初等函数的最凸点,进而刻画了满足一定条件的函数的最凸点的特征,建立了函数最凸点和其一致可导性之间的联系.

介质涂敷导电凸曲面上磁振子辐射场一致性几何绕射理论

本文研究了介质涂敷导电凸曲面上磁振子辐射与绕射一致性高频渐近理论．文中在典型曲面辐射场一致性高频近似解基础上发展了介质涂敷导电凸曲面上磁振子辐射与绕射的一致性几何绕射理论，导出了涂敷导电凸曲面上磁流源高频电磁辐射场的一致性几何绕射理论公式在这个公式中，辐射与绕射场用四个广义Fock型函数表示，深光区这些函数退化为几何光学场。

一类多目标半无限规划的Mond-Weir型对偶

在广义一致局部连通凸函数的约束下,讨论了一类多目标半无限规划的Mond-Weir型对偶,得到了相应的弱对偶、强对偶和逆对偶定理.

参数规划中最优值函数的ε-凹凸性

本文对参数规划问题:■的最优值函数进行了探讨.给出了最优值函数ε-凹凸的若干判别准则.文中许多结果可以被认为是对最优值函数凹凸性研究成果的更一般拓广.

局部性保凸插值基函数的不存在性

本文证明不存在适当的基函数，使得由其混合产生的曲线插值于给定的控制点，并同时具有保凸性．

两类泛函族一致有界原理的统一与推广

本文将广义按范γ－拟次加算子族的一致有界原理与凸泛函族的一致有界原理作了统一与推广．