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Steiner选择和算子的集值扩张(Ⅱ)——对逼近理论的应用

 引用本文: 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[J]. 应用数学和力学, 2002, 23(5): 518-525.
TERAN Pedro, L PEZ-DIAZ MIGUEL. Set-Valued Extension of Operators via Steiner Selections(Ⅱ)-Applications to Approximation[J]. Applied Mathematics and Mechanics, 2002, 23(5): 518-525.
 Citation: TERAN Pedro, L PEZ-DIAZ MIGUEL. Set-Valued Extension of Operators via Steiner Selections(Ⅱ)-Applications to Approximation[J]. Applied Mathematics and Mechanics, 2002, 23(5): 518-525.

## Steiner选择和算子的集值扩张(Ⅱ)——对逼近理论的应用

• 中图分类号: 177.91

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

• 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.
•  [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.
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##### 出版历程
• 收稿日期:  2001-05-20
• 刊出日期:  2002-05-15

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