Strictly convex spaces are important concepts in functional analysis and optimization theory. A strictly convex space is a space in which the line segment connecting any two distinct points lies entirely within the space"s interior. This property ensures that the space has a unique center and is free from any flat or concave surfaces. In mathematics, strictly convex spaces play a crucial role in the study of convex sets, convex functions, and convex optimization problems. They are also widely used in the analysis of optimization algorithms and the convergence of iterative methods. Understanding the properties and applications of strictly convex spaces is essential for researchers and practitioners in the fields of mathematics, engineering, and computer science. Here"s a collection of English sentences and example usages to help illustrate and understand the concept of strictly convex spaces in greater depth.
严格凸空间,strictly convex space
1)strictly convex space严格凸空间
1.Fixed points of nonexpansive mappings instrictly convex spaces;严格凸空间中非扩张映象的不动点级的结构
2.In this paper the properties of thestrictly convex space are studied further.本文进一步研究了严格凸空间的性质，并给出了等距算子为线性算子的一个充分条件。
2)strictly convex Banach space严格凸Banach空间
1.By using point valued for set-valued mappings instrictly convex Banach space,a sufficient and necessary condition for Ishikawa multistep iterative processing with errors for asymptotically quasi-nonexpansive mappings of set-valued to converge to coupled fixed point is proved.在严格凸Banach空间中,用集值映象点值化方法,证明了集值渐近准非扩张映象带误差的三步迭代列收敛于耦合不动点的充要条件。
2.Instrictly convex Banach space,there F(T)is set of coupled fixed points of T for nonexpansive mapping,then F(T)is(closed convex set.在严格凸Banach空间中,研究可点值化集值非扩张映象T的耦合不动点集F(T)的闭凸性。
3.We prove the main result as follows:Let K be a nonempty closed convex subset of astrictly convex Banach space E,T:K→K be a continuous quasi-nonexpanaive mapping,and let T(K) be contained in a compact subset of K,iterative scheme ｛x_n｝~~∞__(n=1)definited as follow:(IS)y_n=(1-β_n)x_n+β_nTx_n,n≥1, x_(n+1)=(1-α_n)x_n+α_nTy_n,n≥1,where｛α_n｝and ｛β_n｝satisfy certain condition,then｛x_n｝c.研究了严格凸Banach空间中非空间凸子集上拟非扩展映象的不动点的迭代逼近问题,主要证明了:设E是严格凸Banach空间,K为E的闭凸子集,T:K→K为连续拟非扩展映象。
英文短句/例句
1.Remarks on K-Strictly Convex Banach Spaces;关于K-严格凸Banach空间的注记
2.Existence and uniqueness for element of best approximation in strict convex Banach spaces;严格凸Banach空间中最佳逼近元的存在与唯一性
3.Some Equivalent Propositions about Strict Convex in Banach Space;Banach空间严格凸的几个等价命题
4.ITERATIVE APPROXIMATION OF LIPSCHITZ STRICTLYPSEUDOCONTRACTIVE MAPPINGS IN UNIFORMLYCONVEX BANACH SPACES;一致凸Banach空间中Lipschitz严格伪收缩映射的迭代逼近
5.Strict Feasibility of Pseudo-monotone Variational Inequality in Banach SpacesBanach空间中伪单调变分不等式的严格可行性
6.A Sufficient Condition on Strict Convexity Space of Real Conjugate Space;实共轭空间X~*严格凸的一个充分条件
7.Differentiability and Approximation of Convex Functions in Banach Spaces;Banach空间中凸函数的微分理论和逼近
8.The Study on the Several Kinds of Convexity and Smoothness in Banach Spaces;Banach空间的几种凸性与光滑性之探讨
9.The Study on the Some Dentablity and Convexity of Banach Spaces;Banach空间若干可凹性与凸性研究
10.The Study on the Some K Convexity and K Smoothness of Banach Spaces;Banach空间若干K凸性与K光滑性的研究
11.U-Property and U-Convex Module in Banach Spaces;Banach空间的U-性质与U-凸模
12.The Modulus of Convexity of Quasi-Banach Space and Special Martingale Inequality;拟Banach空间上的凸性模与特殊鞅不等式
13.Totally Convex Functions and the Proximal Point Algorithm in Banach Spaces;Banach空间的完全凸函数与逼近点算法
14.A equivalent condition of convexity in Banach space;Banach空间凸性的一种等价条件
15.Some Convexities of Banach Space and Their Correlations;Banach空间若干凸性及相互关系
16.Advances in Research for Rotund Norm of Banach Spaces;Banach空间凸性范数研究的若干进展
17.Average Strong Convexity and Its Dual Property in Banach Spaces;Banach空间的平均强凸性及其对偶性
18.The Study of Convexity and Fixed Point Problems in n-Banach Spacesn-Banach空间中凸性与不动点问题的研究
相关短句/例句
strictly convex Banach space严格凸Banach空间
1.By using point valued for set-valued mappings instrictly convex Banach space,a sufficient and necessary condition for Ishikawa multistep iterative processing with errors for asymptotically quasi-nonexpansive mappings of set-valued to converge to coupled fixed point is proved.在严格凸Banach空间中,用集值映象点值化方法,证明了集值渐近准非扩张映象带误差的三步迭代列收敛于耦合不动点的充要条件。
2.Instrictly convex Banach space,there F(T)is set of coupled fixed points of T for nonexpansive mapping,then F(T)is(closed convex set.在严格凸Banach空间中,研究可点值化集值非扩张映象T的耦合不动点集F(T)的闭凸性。
3.We prove the main result as follows:Let K be a nonempty closed convex subset of astrictly convex Banach space E,T:K→K be a continuous quasi-nonexpanaive mapping,and let T(K) be contained in a compact subset of K,iterative scheme ｛x_n｝~~∞__(n=1)definited as follow:(IS)y_n=(1-β_n)x_n+β_nTx_n,n≥1, x_(n+1)=(1-α_n)x_n+α_nTy_n,n≥1,where｛α_n｝and ｛β_n｝satisfy certain condition,then｛x_n｝c.研究了严格凸Banach空间中非空间凸子集上拟非扩展映象的不动点的迭代逼近问题,主要证明了:设E是严格凸Banach空间,K为E的闭凸子集,T:K→K为连续拟非扩展映象。
3)strict convex Banach spaces严格凸Banach空间
1.Existence and uniqueness for element of best approximation instrict convex Banach spaces;严格凸Banach空间中最佳逼近元的存在与唯一性
2.In thestrict convex Banach spaces, we obtained the theory of existence and uniqueness of element of best approximate on compact convex subset.获得了严格凸Banach空间中 ,关于弱紧凸集最佳逼近元的存在与唯一性定
4)strictly convex normed space严格凸赋范空间
5)k-strictly convex spacek-严格凸空间
6)strictly convex space严凸空间
1.On supporting balls by affine sets and the characterizationofstrictly convex spaces;关于仿射集对球的支承与严凸空间的特征
延伸阅读
局部凸空间局部凸空间locally convex space【补注】局部凸空间在遍及分析学的诸领域中大量出现，如测度和积分理论，单变量、多变量或无穷多变量的复分析，偏微分方程，积分方程，逼近论，算子和谱理论，以及概率论.许多序列空间，全纯函数、连续函数或可测函数的空间，测度空间，检验函数和广义函数的空间有自然的局部凸拓扑.强有力的局部凸空间的对偶理论提供了一个重要工具，把关于空间(或关于局部凸空间之间的线性算子)的问题变成关于线性型的问题.对偶理论的基本结果包括双极定理(bipolar山印reln)(lh俪田曲.山定理(Hahn~Banaeht址幻咖)的一种形式)，A】ao梦u-Bourbeki定理(川ao蜘一Bour加kit玩”n二n)(关于对偶中的等度连续集)和Mackey一Arens定理(Mackey-A肥瑙tl拟〕ren。)(刻画与给定的对偶对相容的拓扑的特征).借助于对偶理论，能研究线性算子的满射性质和连续线性右逆的存在性(引向偏微分方程的解算子);想到这些应用，B.n，11a月aMo八oB发展了同调方法.拓扑和有界型性(bomofo留)之间存在抽象的对偶性，而等度连续集提供了紧论(con1Pacto幻留)的一个重要例子.局部凸空间的经典结构理论的一部分可以看成(基本的)llll.ch空间(Banach sPace)理论及其主要定理(它们通常是Hahn~Banach定理和B出re范畴定理(见Bai比定理(加iret坛”rem))的推论)的推广.这方面的发展导致引人一些特殊类型的局部凸空间，其中最重要的类是:Fl食het空间和(DF)空间，桶型空间和有界型空间，自反空间，(LF)空间(即F欢兄het空间的可数归纳极限)，核型空间，Sch-认公rtZ空间和Montel空间.拓扑张量积是作为一种工具引进，用以研究算子空间和矢量值函数与矢量值广义函数的空间.A.Gro-thendiek【A41在这方面探讨了核型空间并提出了逼近问题，它已被P.Enflo〔101解决，他给出了无逼近性质的砌11aeh空间的第一个例子.此后，A.S翻-kowski证明了一个Hilbert空间上所有有界线性算子的空间无逼近性质.除了紧凸集外(Choq”et理论在抽象位势论中有重要应用)，也对弱紧集作了研究(见【A3】).参考文献fAS]一汇A8』是关于局部凸空间和对偶理论的一般性专著.!AI]，IAg」和【A10]专用于更特定的论题，而【A21是关于无穷维全纯论及其与局部凸空间的联系方面的专著.局部凸空间【1.勿~凡，沈;，~“n，。oenP0c冲a“c卿」一种实或复数域上的Hausdorff拓扑向l空间(topofogical研戈tor sPace)，其中零元素的任一邻域包含零元素的一个凸邻域;换言之，拓扑向量空间E是局部凸空间，当且仅当E的拓扑是Ha止司。
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