Baskakov-Durrmeyer算子在Orlicz空间L_Φ~*[0,∞)中逼近的等价定理
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摘要
在由Young函数生成的Orlicz空间L_Φ~*[0,∞)中,考虑Baskakov-Durrmeyer算子的逼近性质.利用修正的K-泛函和连续模等价性,得到了Baskakov-Durrmeyer算子逼近的正、逆和等价定理.
The author considered the approximation properties of the Baskakov-Durrmeyer operators in Orlicz spaces L_Φ~*[0,∞) generated by the Young function,and obtained the direct,inverse and equivalent theorem of the approximation by the Baskakov-Durrmeyer operators by using the equivalence relationship between modified K-functional and continuous modulus.
The author considered the approximation properties of the Baskakov-Durrmeyer operators in Orlicz spaces L_Φ~*[0,∞) generated by the Young function,and obtained the direct,inverse and equivalent theorem of the approximation by the Baskakov-Durrmeyer operators by using the equivalence relationship between modified K-functional and continuous modulus.
引文
[1]Heilmann M.Direct and Converse Results for Operators of Baskakov-Durrmeyer Type[J].Approx Theory Appl,1989,5(1):105-127.
[2]刘喜武,郭顺生,宋占杰.Baskakov-Durrmeyer型算子的带权同时逼近[J].吉林大学自然科学学报,1999(4):21-24.(LIU Xiwu,GUO Shunsheng,SONG Zhanjie.Weighted Simultaneous Approximation of BaskakovDurrmeyer Operators[J].Acta Scientiarum Naturalium Universitatis Jilinensis,1999(4):21-24.)
[3]QI Qiulan,GUO Shunsheng.Simultaneous Approximation by Baskakov-Durrmeyer Operator[J].Chin Quart J of Math,2001,16(1):38-45.
[4]毛梁成.Baskakov-Durrmeyer算子同时逼近[J].宝鸡文理学院学报(自然科学版),2007,27(2):103-106.(MAO Liangcheng.Simultaneous Approximation by Baskakov-Durrmeyer Operators[J].Journal of Baoji University of Arts and Sciences(Natural Science Edition),2007,27(2):103-106.)
[5]郭顺生,宋占杰.Baskakov-Durrmeyer算子的点态逼近[J].数学研究与评论,2001,21(3):441-446.(GUO Shunsheng,SONG Zhanjie.Pointwise Approximation by Baskakov-Durrmeyer Operator[J].Journal of Mathematical Research and Exposition,2001,21(3):441-446.)
[6]杨戈,石宁,徐爱华.关于Baskakov-Durrmeyer算子的强逆逼近[J].河北工程大学学报(自然科学版),2007,24(1):110-112.(YANG Ge,SHI Ning,XU Aihua.Strong Converse Approximation for Baskakov-Durrmeyer Operators[J].Journal of Hebei University of Engineering(Natural Science Edition),2007,24(1):110-112.)
[7]韩领兄,吴嘎日迪,刘国锋.Orlicz空间中加权光滑模与K-泛函的等价性及其应用[J].数学物理学报,2014,34A(1):95-108.(HAN Lingxiong,WU Garidi,LIU Guofeng.The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and Its Application[J].Acta Mathematica Scientia,2014,34A(1):95-108.)
[8]HAN Lingxiong,WU Garidi.Approximation by Modified Summation Integral Type Operators in Orlicz Spaces[J].Applied Mathematics,2017,30(3):613-622.
[9]韩领兄,吴嘎日迪.Gamma算子在Orlicz空间L*Φ(0,∞)中加Jacobi权同时逼近的强逆不等式[J].高校应用数学学报,2016,31A(3):366-378.(HAN Lingxiong,WU Garidi.Strong Converse Inequality of Jacobi Weighted Simultaneous Approximation for Gamma Operators in Orlicz Spaces L*Φ(0,∞)[J].Appl Math J Chinese Univ,2016,31A(3):366-378.)
[10]HE Yuzan.Ba Spaces and Orlicz Spaces[J].Function Spaces and Complex Analysis,1997,2:37-62.
[11]Ditzian Z,Totik V.Moduli of Smoothness[M].New York:Springer-Verlag,1987.
[12]QI Qiulan,GUO Shunsheng,LI Jiankun.Approximation by Modified Summation Integral Type Operators in the Lp Spaces[J].Journal of Mathematical Research and Exposition,2009,29(6):1069-1081.
[13]Ditzian Z,Totik V.K-Functionals and Weighted Moduli of Smoothness[J].J Approx Theory,1990,63(1):3-29.
[2]刘喜武,郭顺生,宋占杰.Baskakov-Durrmeyer型算子的带权同时逼近[J].吉林大学自然科学学报,1999(4):21-24.(LIU Xiwu,GUO Shunsheng,SONG Zhanjie.Weighted Simultaneous Approximation of BaskakovDurrmeyer Operators[J].Acta Scientiarum Naturalium Universitatis Jilinensis,1999(4):21-24.)
[3]QI Qiulan,GUO Shunsheng.Simultaneous Approximation by Baskakov-Durrmeyer Operator[J].Chin Quart J of Math,2001,16(1):38-45.
[4]毛梁成.Baskakov-Durrmeyer算子同时逼近[J].宝鸡文理学院学报(自然科学版),2007,27(2):103-106.(MAO Liangcheng.Simultaneous Approximation by Baskakov-Durrmeyer Operators[J].Journal of Baoji University of Arts and Sciences(Natural Science Edition),2007,27(2):103-106.)
[5]郭顺生,宋占杰.Baskakov-Durrmeyer算子的点态逼近[J].数学研究与评论,2001,21(3):441-446.(GUO Shunsheng,SONG Zhanjie.Pointwise Approximation by Baskakov-Durrmeyer Operator[J].Journal of Mathematical Research and Exposition,2001,21(3):441-446.)
[6]杨戈,石宁,徐爱华.关于Baskakov-Durrmeyer算子的强逆逼近[J].河北工程大学学报(自然科学版),2007,24(1):110-112.(YANG Ge,SHI Ning,XU Aihua.Strong Converse Approximation for Baskakov-Durrmeyer Operators[J].Journal of Hebei University of Engineering(Natural Science Edition),2007,24(1):110-112.)
[7]韩领兄,吴嘎日迪,刘国锋.Orlicz空间中加权光滑模与K-泛函的等价性及其应用[J].数学物理学报,2014,34A(1):95-108.(HAN Lingxiong,WU Garidi,LIU Guofeng.The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and Its Application[J].Acta Mathematica Scientia,2014,34A(1):95-108.)
[8]HAN Lingxiong,WU Garidi.Approximation by Modified Summation Integral Type Operators in Orlicz Spaces[J].Applied Mathematics,2017,30(3):613-622.
[9]韩领兄,吴嘎日迪.Gamma算子在Orlicz空间L*Φ(0,∞)中加Jacobi权同时逼近的强逆不等式[J].高校应用数学学报,2016,31A(3):366-378.(HAN Lingxiong,WU Garidi.Strong Converse Inequality of Jacobi Weighted Simultaneous Approximation for Gamma Operators in Orlicz Spaces L*Φ(0,∞)[J].Appl Math J Chinese Univ,2016,31A(3):366-378.)
[10]HE Yuzan.Ba Spaces and Orlicz Spaces[J].Function Spaces and Complex Analysis,1997,2:37-62.
[11]Ditzian Z,Totik V.Moduli of Smoothness[M].New York:Springer-Verlag,1987.
[12]QI Qiulan,GUO Shunsheng,LI Jiankun.Approximation by Modified Summation Integral Type Operators in the Lp Spaces[J].Journal of Mathematical Research and Exposition,2009,29(6):1069-1081.
[13]Ditzian Z,Totik V.K-Functionals and Weighted Moduli of Smoothness[J].J Approx Theory,1990,63(1):3-29.