Steiner选择和算子的集值扩张(Ⅱ)——对逼近理论的应用

皮佐尔·特尔文; 米古尔·拉皮兹·迪亚兹

Steiner选择和算子的集值扩张(Ⅱ)——对逼近理论的应用

西班牙奥威索大学, s/n 33007 奥威索, 西班牙

基金项目: 西班牙FPI基金资助课题(98-71701353号);DGES基金资助课题(PB98-1534);DGESIC基金资助课题(PB97-1286)

详细信息

中图分类号: 177.91
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出版历程
- 收稿日期: 2001-05-20
- 刊出日期: 2002-05-15

Set-Valued Extension of Operators via Steiner Selections(Ⅱ)-Applications to Approximation

Facultad de Ciencias, Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007 Oviedo, Spain

摘要

摘要: 在(Ⅰ)的基础上,得出对集值函数逼近理论的某些应用:Korovkin型定理,一种将经典逼近算子扩张到集值族的方法,以及Jackson估算.
- 集值扩张 /
- Steiner选择 /
- Jackson估算
Abstract: On the basis of Part(Ⅰ) of this series some applications to the approximation of set-valued functions are obtained: Korovkin type theorems,a method to extend classical approximation operators to the set-valued setting and a Jackson type estimate.
- set-valued extension /
- Steiner selection /
- a Jackson type estimate

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参考文献(23)

[1]	皮佐尔特尔文,米古尔拉皮兹*迪亚兹.Steiner选择和算子的集值扩张(Ⅰ)-理论结果[J].应用数学和力学,23(5):507-517.
[2]	Korovkin P P.On convergence of linear positive operators in the space of continuous functions[J].Doklady Akad Nauk SSSR(N S),1953,90:961-964.
[3]	Korovkin P P.Linear operators and approximation theory[A].In:Russian Monographs and Texts on Advanced Mathematics and Physics[C].Vol.Ⅲ.New York:Gordon and Breach Publishers Inc,1959,Delhi:Hindustan Publishing Corp,Delhi 1960.(English version)
[4]	Altomare F,Campiti M.Korovkin Type Approximation Theory and Its Applications.In:De Gruyter Studies in Mathematics[M].Vol.17,Berlin/New York:De Gruyter,1994.
[5]	Altomare F.Lototsky-Schnabl operators on the unit interval and degenerate diffusion equations[A].In:Progress in Functional Analysis[C].Peniscola,1990,North-Holland Math,Stud,170,Amsterdam:North-Holland,1992,259-277.
[6]	Altomare F.On some approximation processes and their associated parabolic problems[J].Rend Sem Mat Fis Milano,1994,61:231-255.
[7]	Clement P,Timmermans C A.On C0-semigroups generated by differential operators satisfying ventcel's boundary conditions[J].Nederl Akad Wetensch Inday Math,1986,48:379-387.
[8]	Favini A,Fuhrman M.Approximation results for semigroups generated by multivalued linear operators and applications[J].Differential Integral Equations,1998,11:781-805.
[9]	Roth W.Korovkin approximation for weighted set-valued functions[J].J Approx Theory,1999,100:94-112.
[10]	Keimel K,Roth W.A Korvkin type approximation theorem for set-valued functions[J].Proc Amer Math Soc,1988,104:819-924.
[11]	Campiti M.A Korovkin type theorem for set-valued Hausdorff continuous functions[J].Matematiche(Catania),1987,42(1-2):29-35.
[12]	Vitale R A.Approximation of convex set-valued functions[J].J Approx Theory,1979,26:301-316.
[13]	Wulbert D E.Convergence of operators and Korovkin's theorem[J].J Approx Theory,1968,1:381-390.
[14]	Lorentz G C.Bernstein Polynomials[M].New York:Chelsea Publishing Co,1986.
[15]	Adell J A,Cal J.De la Bernstein-type operators diminish the φ-variation[J].Constr Approx,1996,12:489-507.
[16]	Neven J.Discrete-Parameter Martingales North-Holland Mathematical Library[M].Vol.10,Amsterdam-Oxford:North-Holland Publishing Co,1975.
[17]	Varadhan S R S.Lectures on Diffusion Problems and Partial Differential Equations[M].In:Tata Institute of Fundamental Research Lectures on Mathematics and Physics,64,Bombay:Tata Institute of Fundamental Research,1980.
[18]	Sikkema P C.Der wert einiger konstanten in der theorie der approximation mit bernstein-polynomen[J].Numer Math,1961,3:107-116.
[19]	Annastasiou G A,Cottin C,Gonska H.Global smoothness of approximation operators[J].Analysis,1991,11:43-57.
[20]	Brown B M,Elliott D,Paget D F.Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function[J].J Approx Theory,1987,49:196-199.
[21]	Lindvall T.Bernstein polynomials and the law of large numbers[J].Math Scientist,1982,7:127-139.
[22]	Nikolskii S N.Jackson's order of approximation in the problem of approximation of continuous set-valued map[J].Math Balkanica,1991,4:396-400.
[23]	Artstein Z.Piecewise linear approximations of set-valued maps[J].J Approx Theory,1989,56:41-47.