Bernstein-Durrmeyer算子拟中插式在Orlicz空间中的逼近
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摘要
本文在Orlicz空间中研究了Bernstein-Durrmeyer算子拟中插式B_n~(2r-1)(f,x)逼近性质.利用2r阶Ditzian-Totik模与K-泛函的等价性,Jensen不等式,H?lder不等式,Berens-Lorentz引理得到了逼近的正,逆和等价定理,从而推广了Bernstein-Durrmeyer算子拟中插式B_n~(2r-1)(f,x)在L_P空间的逼近结果.
In the present paper,we will study the approximation property of the BernsteinDurrmeyer quasi-interpolants B_n~(2r-1)(f,x) in Orlicz space. By using the 2r-th Ditzian-Totik modulus of smoothness,Jensen inequality,H?lder inequality and Berens-Lorentz lemma,we obtain the direct,inverse and equivalence theorems,which generalize the approximation results of the Bernstein-Durrmeyer quasi-interpolants B_n~(2r-1)(f,x) in LPspace.
In the present paper,we will study the approximation property of the BernsteinDurrmeyer quasi-interpolants B_n~(2r-1)(f,x) in Orlicz space. By using the 2r-th Ditzian-Totik modulus of smoothness,Jensen inequality,H?lder inequality and Berens-Lorentz lemma,we obtain the direct,inverse and equivalence theorems,which generalize the approximation results of the Bernstein-Durrmeyer quasi-interpolants B_n~(2r-1)(f,x) in LPspace.
引文
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[2]汪和平.Orlicz空间上的多项式逼近[D].北京:北京师范大学,1993.
[3]赵德钧.一类Bernstein型算子加权逼近[J].数学杂志,2000,20(3):293–299.
[4]刘清国,刘军.Bernstein-Sheffer算子的逼近等价定理[J].数学杂志,2003,23(2):253–256.
[5]李翠香,任孟霞.Bernstein-Kantorovich算子的迭代布尔和的逼近性质[J].数学杂志,2007,27(1):105–110.
[6]Ditzian Z,Ivanov K.Bernstein-type operators and their derivatives[J].J.Approx.The.,1989,56:72–90.
[7]郭顺生,张更生,齐秋兰,刘丽霞.Bernstein-Durrmeyer算子拟中插式的逼近[J].数学学报,2005,48(4):681–692.
[8]Duan Liqin,Cuixiang.The global approximation by left-Bernstein-Durrmeyer quasi-interpolants in L p[0,1][J].Anal.The.Appl.,2004,20(3):242–251.
[9]Sablonni`ere P.Representation of quasi-interplants as differential operators and applications[J].Intern.Ser.Numer.Math.,1999,132:233–252.
[10]Ditzian Z,Totik V.Moduli of smoothness[M].New York:Springer-Verlag,1987.
[11]Lorentz G G.On the theory of spacesΛ[J].Pacific J.Math.,1951,1:411–429.
[2]汪和平.Orlicz空间上的多项式逼近[D].北京:北京师范大学,1993.
[3]赵德钧.一类Bernstein型算子加权逼近[J].数学杂志,2000,20(3):293–299.
[4]刘清国,刘军.Bernstein-Sheffer算子的逼近等价定理[J].数学杂志,2003,23(2):253–256.
[5]李翠香,任孟霞.Bernstein-Kantorovich算子的迭代布尔和的逼近性质[J].数学杂志,2007,27(1):105–110.
[6]Ditzian Z,Ivanov K.Bernstein-type operators and their derivatives[J].J.Approx.The.,1989,56:72–90.
[7]郭顺生,张更生,齐秋兰,刘丽霞.Bernstein-Durrmeyer算子拟中插式的逼近[J].数学学报,2005,48(4):681–692.
[8]Duan Liqin,Cuixiang.The global approximation by left-Bernstein-Durrmeyer quasi-interpolants in L p[0,1][J].Anal.The.Appl.,2004,20(3):242–251.
[9]Sablonni`ere P.Representation of quasi-interplants as differential operators and applications[J].Intern.Ser.Numer.Math.,1999,132:233–252.
[10]Ditzian Z,Totik V.Moduli of smoothness[M].New York:Springer-Verlag,1987.
[11]Lorentz G G.On the theory of spacesΛ[J].Pacific J.Math.,1951,1:411–429.