共查询到20条相似文献,搜索用时 15 毫秒
1.
本文研究了Gurarii的凸性模与正规结构的联系.利用关于该模的不等式得出了如果存在ε,1≤ε≤2,使得β(ε)>ε-1.则空间X具有一致正规结构. 相似文献
2.
Satit Saejung 《数学物理学报(B辑英文版)》2011,31(3):1035-1040
We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters U~ax(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. 相似文献
3.
B. Zlatanov 《数学物理学报(B辑英文版)》2011,31(2):576-590
In this note, we investigate the generalized modulus of convexity δ ( λ ) and the generalized modulus smoothness ρ ( λ ) . We obtain some estimates of these moduli for X = lp . We obtain inequalities between WCS coefficient of a K¨othe sequence space X and δ ( λ ) X . We show that, for a wide class of K¨othe sequence spaces X, if for some ε∈ (0, 9 10 ] holds δ X (ε) > 1 3 1 √ 3 2 ε, then X has normal structure. 相似文献
4.
Satit Saejung 《Journal of Mathematical Analysis and Applications》2008,337(1):123-129
We present some sufficient conditions for normal structure of Banach spaces and their dual spaces in terms of the characteristic of convexity, the James constant, and the coefficient of weak orthogonality. Many known results are improved and strengthened. We also show that some of our results are sharp. 相似文献
5.
V. Preda 《Mathematical Methods of Operations Research》1992,36(6):547-563
We extend the duality theorems for a class of nondifferentiable problems with Mond-Weir type duals. 相似文献
6.
Generalized monotonicity and generalized convexity 总被引:2,自引:0,他引:2
S. Komlósi 《Journal of Optimization Theory and Applications》1995,84(2):361-376
Generalized monotonocity of bifunctions or multifunctions is a rather new concept in optimization and nonsmooth analysis. It is shown in the present paper how quasiconvexity, pseudoconvexity, and strict pseudoconvexity of lower semicontinuous functions can be characterized via the quasimonotonicity, pseudomonotonicity, and strict pseudomonotonicity of different types of generalized derivatives, including the Dini, Dini-Hadamard, Clarke, and Rockafellar derivatives as well.This research was supported by the National Science Foundation of Hungary, Grant No. OTKA 1313/1991. 相似文献
7.
Shen Yu-Liang 《Proceedings of the American Mathematical Society》1996,124(6):1879-1882
We will discuss the geometry of the unit sphere in the Banach space of integrable holomorphic quadratic differentials on a Riemann surface and answer some questions posed by L.R. Goldberg (Proc. Amer. Math. Soc. 118 (1993), 1179--1185).
8.
高继 《应用泛函分析学报》2000,2(3):247-263
假设S(X)是Banach空间X的单位球面,作引进了四个新的几何参数:Jε(X)=sup{βε(x),x∈S(X)},jε(X)=inf{βε(x),x∈S(X)},Gε(X)=sup{αε(x),x∈S(X)},gε(X)=inf{αε(x),x∈S(S)},其中≤ε≤1,βε(x)=sup{min{‖x εy‖,‖x-εy‖,y∈S(X)}},αε(x)=inf{max{‖x εy‖,‖x-εy‖,y∈S(X)}},讨论了这些参数的性质,本主要结果是:如果主要结果是:如果有一个ε,0≤ε≤1,使得Jε(X)<1 ε/2或gε(X)>1 ε/3,那末X有一至正规结构。 相似文献
9.
Ji Gao 《Periodica Mathematica Hungarica》2005,51(2):19-30
Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"10"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"11"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"12"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"13"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>X$
be a real Banach space and $S(X) = \{x \in X: \|x\| = 1\}$ be the unit sphere of $X$. The parameters $E_{\epsilon}(X)=\sup\{\alpha_{\epsilon}(x):
x \in S(X)\}$, $e_{\epsilon}(X)=\inf\{\alpha_{\epsilon}(x): x \in S(X)\}$, $F_{\epsilon}(X)=\sup\{\beta_{\epsilon}(x): x \in
S(X)\}$, and $f_{\epsilon}(X)=\inf\{\beta_{\epsilon}(x): x \in S(X)\}$, where $\alpha_{\epsilon}(x) = \sup\{\| x + \epsilon
y \|^{2}+ \| x - \epsilon y \|^{2}: y \in S(X)\}$ and $\beta_{\epsilon}(x) = \inf\{\| x + \epsilon y \|^{2}+ \| x - \epsilon
y \|^{2}: y \in S(X)\}$, are defined and studied. The main result is that a Banach space $X$ with $E_{\epsilon}(X) < 2 + 2\epsilon
+\frac{1}{2}\epsilon^{2}$ for some $0\leq \epsilon \leq 1$ has uniform normal structure. 相似文献
10.
Criteria for locally uniform convexity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz function spaces generated by locally uniformly convex Banach space, locally uniform convexity and strict convexity are equivalent. 相似文献
11.
It is known that, given a Banach space , the modulus of convexity associated to this space is a non-negative function, non-decreasing, bounded above by the modulus of convexity of any Hilbert space and satisfies the equation for every , where is a constant. We show that, given a function satisfying these properties then, there exists a Banach space in such a way its modulus of convexity is equivalent to , in Figiel's sense. Moreover this Banach space can be taken to be two-dimensional.
12.
Optimality and duality with generalized convexity 总被引:4,自引:0,他引:4
N. G. Rueda M. A. Hanson C. Singh 《Journal of Optimization Theory and Applications》1995,86(2):491-500
Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given. 相似文献
13.
B. Zlatanov 《Journal of Mathematical Analysis and Applications》2008,341(2):1042-1054
It is proved that a weighted Orlicz sequence space ?M(w), equipped with Luxemburg or Amemiya norm has weak uniform normal structure iff ?M(w)≅hM(w) for wide class of weight sequences . An example is constructed, where M has not Δ2-condition but by choosing a suitable weight sequence limn→∞wn=∞ we get that ?M(w) has weak uniform normal structure. 相似文献
14.
We shall introduce a new geometric constant A(X) of a Banach space X,which is closely related to the modulus of smoothness ρX(τ),and investigate it in relation with the constant A2(X) by Baronti et al.,the von Neumann–Jordan constant CNJ(X) and the James constant J(X).A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved. 相似文献
15.
Anurag Jayswal Ioan Stancu-Minasian 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):616-625
In this paper, we are concerned with a class of nondifferentiable minimax programming problems and its two types of higher-order dual models. We establish weak, strong and strict converse duality theorems in the framework of generalized convexity in order to relate the optimal solutions of primal and dual problems. Our study improves and extends some of the known results in the literature. 相似文献
16.
L.Y Nikolova 《Journal of Mathematical Analysis and Applications》2003,283(2):549-556
We show how uniform convexity can be preserved in the logarithmic spaces Aθ(logA)b,p. Estimates are given for the moduli of convexity of Aθ(logA)b,p in terms of the moduli of A0 and A1, when one or both of them are uniformly convex. 相似文献
17.
LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting
. In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242. 相似文献
18.
We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of
convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical
Banach spaces. An application to geometry of normed spaces is also indicated. 相似文献
19.
曾小林 《应用泛函分析学报》2012,14(1):23-31
致力于随机一致凸性概念的进一步探讨.首先,通过一个特殊的层次剖分指出对任意的随机赋范模而言随机凸性模都有良好定义,从而改进了近期的文献中许多已知的结果.然后,提出并研究了一种与随机一致凸性密切相关的新性质,从一个新的角度阐述了随机一致凸性的复杂性. 相似文献
20.
In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second
order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established.
Our study naturally unifies and extends some previously known results on minimax programming. 相似文献