查询词典 uniformly convex

Next,it proves that if E is a barrelled space and F〓 is a locally convex space,Kis all the compact operators of L,then the weak operator topology and the uniformly operator topology have the same sub-series convergence series in Kif and only if 〓 contains no copyof 〓.

其次又得到，若E是桶型空间，〓是局部凸空间，那么紧算子空间K中弱算子拓扑与一致算子拓扑具有相同子级数收敛的充要条件是〓不拓扑同胚地包含〓。

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed spacer and obtains a fixed point theorem in metric linear spaces.

摘要证明了完备的一致局部半凸概率赋范空间上的概率压缩映象必有唯一不动点，得到了一类度量线性空间中关于伪范数族一致压缩映象的不动点定理。

In the first pa.rt,we clolinc the TC inodnhis of convexity and TC modulus of smoothness of quasi-Baiiach space, and prove that the space which is characterized by uniform convexity is same as the space which is cliaracteri/,ed by uniform TC convcxity.Then we give several characterizations of q-uniformly TC convex quasi-Banach space.At the same time ,we prove the triionned-theorcm.In the second part, we give the relationships between some inequalities of martingales with values in quasi-Banach space and uniformly TC convex quasi-Banach space.

本文分四部分，第一部分在拟Banach空间上定义了TC凸性模和TC光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是一致的，即Banach空间X是一致TC凸的的充分必要条件是它是一致凸的，Banach空间X是一致TC光滑的充分必要条件是它是一致光滑的，还分别得出了判定一致TC凸和一致TC光滑的几个充分必要条件，同时还证明了在拟范数下的重赋范定理。

In this paper,several quasi-Newton algorithms are generalized to a class of new quasi-Newton equation,several modified quasi-Newton algorithm s are obtained and their global convergence are proved under the objective function is uniformly convex.

将几个拟牛顿算法推广到一类新拟牛顿方程，得到几个修正拟牛顿算法；在目标函数为一致凸的条件下，证明了它们都具有全局收敛性。

Under certain conditions, we prove the global convergence of the modified Broydens class of quasi-Newton methods for solving uniformly convex minimization problems.

并证明算法用于求解一致凸函数极小化问题时的全局收敛性。

There are very sophisticated randomized algorithms for convex and non-convex optimization that rely on recently-developed methods for approximately generating uniformly distributed random variables on convex sets.

有一些关于凸型和非凸型最优化的非常复杂的随机算法，它们依赖于最近研究出的一些方法，在凸型集合中近似地产生平均分布的随机变量。

Based on some results given by K Tan and H K Xu[1] proved, the convergence of three-step iterations of uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space had proved.

引入一致李普希兹的概念，然后在一些已有结果的基础上，证明一致凸Banach空间的紧子集上的一致李普希兹渐进非扩张映射的三步迭代序列的收敛问题。

Inspired by these results, in this paper, we first give the definition of a new mapping ? uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space, then construct three-step iterative sequences of uniformly Lipschitz asymptotically nonexpansive mapping in this subset . We proved the convergence of this three-step iterative sequences for uniformly Lipschitz asymptoticallynonexpansive mapping, Further more, we proved this three-step iterative sequences with an error member converge to fixed points.

从中得到启发，在本文我们首先定义了一致凸Banach空间某非空紧子集上的一种新的映射——一致李普希兹渐进非扩张映射，在该紧子集上构造关于一致李普希兹渐进非扩张映射的三步迭代序列以及具误差的三步迭代序列，先来讨论三步迭代序列的收敛性，进而讨论具误差的三步迭代序列的收敛性。

In the fourth part, we study the growth velocity of q-mean square function of trigonometric martingales, using these we characterize TP q-uniformly convex of the space.

第四部分研究了q均方函数的增长速度与q一致TP可凸性的关系，从而用它们刻划了Banach空间的q一致TP可凸性。

In the second part, we give the relationships between some inequalities of trigonometric martingales with values in Banach space and TP uniform convexity of the space. So we characterize the TP q-uniformly convex of the Banach space by inequalities of trigonometric martingales with values in Banach space.

第二部分研究了取值于Banach空间的一类特殊而义具体的鞅-—三角鞅，三角鞅不等式与该空间的q一致TP凸性的关系，从而用三角鞅不等式刻划了空间的q一致TP可凸性。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。