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1.
切片与Banach空间的凸性,光滑性   总被引:14,自引:1,他引:13  
方习年  王建华 《数学杂志》1999,19(3):293-298
本文用单位球的切片统一且简捷地处理Banach空间的(局部)K一致凸、近一致凸、近一致光滑性;定义Banach空间的(局部)K一致光滑、局部近一致凸、局部近一致光滑、近-强凸、近-强光滑性等概念,并讨论上述凸性,光滑性的关系及性能。  相似文献   

2.
This article has two purposes:the first is to give some structure results for the class of m-isometries,and the second purpose is to extend the notions of left and right inverses to m-left and m-right ...  相似文献   

3.
关于Banach空间的k-光滑性   总被引:3,自引:0,他引:3  
魏文展  程庆进  董鸽 《数学杂志》2006,26(3):292-296
本文研究了k-光滑的Banach空间,引入了k-G可微性的概念.得到了k-光滑的Banach空间的几个等价条件.  相似文献   

4.
The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.  相似文献   

5.
张娟  李庶民 《数学杂志》2016,36(1):55-68
本文主要研究了一类非光滑齐次优化问题(HOP).通过运用Clarke次微分的广义欧拉恒等式获得了使得(HOP)问题的最优解成为KKT点的充分条件并给出了(HOP)问题与(HOP)问题的KKT点及最优解之间的等价刻画.本文的结果是文[1]中已有结果的推广.文中还举例说明了结果的正确性.  相似文献   

6.
Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.  相似文献   

7.
In this paper, we prove that(X, p) is separable if and only if there exists a w~*-lower semicontinuous norm sequence {pn}n=1~∞ of(X~*, p) such that(1) there exists a dense subset Gn of X~* such that pn is Gateaux differentiable on Gn and dpn(Gn) ? X for all n ∈ N;(2) pn ≤ p and pn → p uniformly on each bounded subset of X~*;(3) for anyα∈(0, 1), there exists a ball-covering {B(xi,n~*, r  相似文献   

8.
本文研究带不等式和等式约束的多目标规划的Mond-Weir型对偶性理论。在目标和约束是广义凸的假设下,证明了弱对偶定理、直接对偶定理以及逆对偶定理  相似文献   

9.
The present paper is devoted to determining the metric g for an n-dimension-al (n≥4) Riemannian manifold (M, g) of quasi-constant curvature [1]. By the way, we have identified the space of quasi-constant curvature with the κ-special conformally flat space of K.Yano & B.Y.Chen [8]. Based upon the results so obtained, we have completely determined the canonical metric for such a space to admit the relevant field X as geodesic field, and the geometric structure for (M, g) to be a recurrent space of quasi-constant curvature. Also we have examined the validity of our results just obtained for a 3-dimensional conformally flat space of quasi-constant cvrvature. Besides, we have deduced some global properties of a complete manifold of quasi-constant curvature, which may be useful in applications.  相似文献   

10.
Clarkson不等式与Banach空间几何   总被引:2,自引:2,他引:0  
黄海军 《数学杂志》2001,21(2):173-177
我们证明了Banach空间X是Clarkson p型(q余型)当且仅当X是一个特殊的p一致光滑空间(q-一致凸空间(),我们还找到刻划型(余型)的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。  相似文献   

11.
《Quaestiones Mathematicae》2013,36(3-4):311-318
Abstract

We obtain some results concerning the notions of hypercyclicity and supercyclicity for continuous homogeneous polynomial maps in Banach spaces. We also present a generalization of a theorem due to Beauzamy concerning the existence of orbits tending to infinity for continuous linear operators with spectral radius > 1.  相似文献   

12.
§1.Forthesystemx=-y+δx+lx2+ny2=P(x,y),y=x(1+ax-y)=Q(x,y),{(1.1)wecanfindin[1]thefolowing:ConjectureI.Assume1a<0,n>1,n+l>0,na2...  相似文献   

13.
61. Introduction and PreliminariesLet C be a nonempty subset Of a Banal spare X. Then a mapping T: C -- C is saidto be a LiPSdrizian maPPing if, for ear integer n 2 1, there eallts a constant km > 0' such that Ilaal ~ chill S k.llx ~ all for all ale E C. A Lipschitzian mapping T is saidto be ~ k-LiPSdszian if km = k for all n 2 1, nonerpansive if km = 1 for alln 2 1, eleCtively. Moreover, a maPPing T: C - C is called asymptotically regularll'191if Asllgu 'z ~ chill = 0 for all 2 E…  相似文献   

14.
本文利用“强极小锥”的概念,获得了Banach空间中非线性脉冲Volterra型积分方程整体解的存在性定理,改进了现有文献中的某些结果.  相似文献   

15.
曹广福  邹承祖 《数学杂志》1993,13(3):325-330
本文主要研究了 Banach 空间上交换算子组的张量积以及 Banach 代数的张量积中交换元组的 Taylor 联合谱,推广了 Vasilescu,F.H.及 Wrobel,V.等人结果。  相似文献   

16.
李泽民(1990)将R^n中的极值问题的Kuhu-Tucker条件推广到了线性拓扑空间中的向量极值问题.本文作者从另一角度,以锥为工具,把在概率论与鞅论等学科有着广泛应用的R中的著名的Jensen不等式推广到序Banach空间,导出向量值的Bochner积分型的广义Jensen不等式,从而推广了前人的工作.  相似文献   

17.
ZhongHuaijie 《数学研究》1994,27(1):204-208
We generalize Kadec‘s and Yan Zikun‘s resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.  相似文献   

18.
《随机分析与应用》2013,31(3):455-460
It is shown that every contractive mapping on a probabilistic Banach space has a unique fixed point.  相似文献   

19.
通过构造单调迭代序列,研究了Banach空间中非线性积分微分方程在Sturm边值条件下的最大解与最小解的存在性及其迭代求法。  相似文献   

20.
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