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Monotonicity and best approximation in Banach Lattices

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Acta Mathematica Sinica,English Series 2009年第5期25卷 785-794页

作者： Shu Tao CHEN Xin HE H. HUDZIK Department of Mathematics Harbin Normal University Harbin 150080 P. R. China Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznan Poland

Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi... 详细信息

关键词： Banach lattice uniform monotonicity strict monotonicity upper （lower） locally uniform monotonicity best approximation

ON M-IDEALS AND best approximation

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Acta Mathematicae Applicatae Sinica 1994年第2期10卷 213-219页

作者：韩德广 Department of Mathematics Qufu Normal University Qufu China

In this paper we will prove some theorems on the M-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].

关键词： M-ideal best approximation compact operator.

SOME GENERALIZATIONS OF KY FAN'S best approximation THEOREM

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Analysis in Theory and Applications 2004年第2期20卷 189-198页

作者： A.R.Khan N.Hussain A.B.Thaheem King Fahd University of Petroleum and Minerals Saudi ArabiaBahauddin Zakaria University PakistanKind Fahd University of Petroleum and Minerals Saudi Arabia

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map stud... 详细信息

关键词： best approximation fixed point * -nonexpansive multivalued map almost quasi-convex function metrizable topological vector space hyperconvex space

A Class of Iteration Method for the best approximation Problems

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Advances in Manufacturing 1998年第1期 18-24页

作者： Wang Deren Zhao Fengguang (College of Sciences)

We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .

关键词： best approximation Chebyshev alternating point set Remes method

On best approximations from RS-sets in Complex Banach Spaces

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Acta Mathematica Sinica,English Series 2005年第1期21卷 31-38页

作者： ChongLI DepartmentofMathematics ZhejiangUniversityHangzhou310027P.R.China

The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong ... 详细信息

关键词： Complex RS–set best approximation Uniqueness Strong uniqueness

QUASI-MODULUS OF CONTINUITY AND best approximationS

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数学研究 1994年第1期 154-157页

作者： Qiu Shuxi(Dept. of Math., Xiamen Univ.Xiamen 361005)

ＱＵＡＳＩ－ＭＯＤＵＬＵＳＯＦＣＯＮＴＩＮＵＩＴＹＡＮＤＢＥＳＴＡＰＰＲＯＸＩＭＡＴＩＯＮＳ￥ＱｉｕＳｈｕｘｉ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＸｉａｍｅｎＵｎｉｖ．Ｘｉａｍｅｎ３６１００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ... 详细信息

ＱＵＡＳＩ－ＭＯＤＵＬＵＳＯＦＣＯＮＴＩＮＵＩＴＹＡＮＤＢＥＳＴＡＰＰＲＯＸＩＭＡＴＩＯＮＳ￥ＱｉｕＳｈｕｘｉ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＸｉａｍｅｎＵｎｉｖ．Ｘｉａｍｅｎ３６１００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒａｃｏｎｃｅｐｔｏｆｔｈ...

关键词： Quasi-modulus of continuity best approximation Lipschitz classes.

THE SHARP JACKSON INEQUALITY FOR L^2-approximation ON THE PERIODIC CYLINDER

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Acta Mathematica Scientia 2015年第2期35卷 375-382页

作者：谷懿刘永平 School of Mathematical Sciences Beijing Normal University

We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1（f）2≤κn,m（τ,r）ωr（f,t）2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ （cos θ）（n ∈ N）.

关键词： Jackson inequality best approximation modulus of continuity weight function

On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

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Acta Mathematica Sinica,English Series 2007年第1期23卷 65-76页

作者： Xin Tao YE Chong LI Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China Department of Mathematics Nanjing Xiaozhuang Institute Nanjing 210038 P. R. China Department of Mathematics Zhejiang University Hangzhou 310027 P R China

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.

关键词： system of convex inequalities basic constraint qualification Abadie constraint qualification best approximation

VARIATIONAL L^q-approximation BY VARISOLVENT FAMILY UNDER THE YOUNG'S CONDITION

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Acta Mathematica Scientia 1997年第3期17卷 330-340页

作者：罗祖华 Dept. of Mathematics & Computer Science University of Leicester Leicester LE1 5BH U.K.

The new Lq approximation methods proposed by A.Pinkus and O.Shisha,which maintains the characteristic feature-alternation-of the classic Chebyshev uniform approximation, is extended to varisolvent approximation under the Young's condition.The theorems of existence, characterizations, unicity, de La Vallee Poussin and continuity of the best approximation are presented.

关键词： Varisolvency Young's condition best approximation Property Z