修正Durrmeyer型Bernstein-Stancu算子的逼近
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摘要
研究了一种新近引入的修正Durrmeyer型Bernstein-Stancu算子在[0,1]区间上的逼近性质,建立了点态逼近的正、逆定理.
Recently,DONG et al introduced a new kind of Durrmeyer type Bernstein-Stancu operators,and investigated the approximation properties of the new operators on a subset of[0,1].In this paper,we obtained both the direct and converse results of the approximation by the operators on the whole interval[0,1].
Recently,DONG et al introduced a new kind of Durrmeyer type Bernstein-Stancu operators,and investigated the approximation properties of the new operators on a subset of[0,1].In this paper,we obtained both the direct and converse results of the approximation by the operators on the whole interval[0,1].
引文
[1]GADJIEV A D,GHORBANALIZACH A M.Approximation properties of a new type BernsteinStancu polynomials of one and two variables[J].Applied Mathematics Computation,2010,216(3):890-901.
[2]STANCU D D.Approximation of functions by a new class of linear polynomial operators[J].Revue Roumaine de Mathematiques Pures et Appliquees,1968,13(8):1173-1194.
[3]WANG M L,YU D S,ZHOU P.On the approximation by operators of Bernstein-Stancu types[J].Applied Mathematics Computation,2014,246(11):79-87.
[4]DONG L X,YU D S,ZHOU P.Pointwise approximation by a Durrmeyer variant of BernsteinStancu operators[J].Journal of Inequality Applications,2017(1):28.Doi:10.1186/S13660-016-1291-x.
[5]DITZIAN Z,TOTIK V.Moduli of Smoothness[M].Berlin/New York:Springer-Verlag,1987.
[6]ACAR T,ARAL A,GUPTA V.On approximation properties of a new type Bernstein-Durrmeyer operators[J].Mathetical Slovaca,2015,65(5):1107-1122.
[7]GUO S,LIU L.The pointwise estimate for modified Bernstein operators[J].Studia Scientiarum Mathematicarum Hungarica,2001,37(1):69-81.
[2]STANCU D D.Approximation of functions by a new class of linear polynomial operators[J].Revue Roumaine de Mathematiques Pures et Appliquees,1968,13(8):1173-1194.
[3]WANG M L,YU D S,ZHOU P.On the approximation by operators of Bernstein-Stancu types[J].Applied Mathematics Computation,2014,246(11):79-87.
[4]DONG L X,YU D S,ZHOU P.Pointwise approximation by a Durrmeyer variant of BernsteinStancu operators[J].Journal of Inequality Applications,2017(1):28.Doi:10.1186/S13660-016-1291-x.
[5]DITZIAN Z,TOTIK V.Moduli of Smoothness[M].Berlin/New York:Springer-Verlag,1987.
[6]ACAR T,ARAL A,GUPTA V.On approximation properties of a new type Bernstein-Durrmeyer operators[J].Mathetical Slovaca,2015,65(5):1107-1122.
[7]GUO S,LIU L.The pointwise estimate for modified Bernstein operators[J].Studia Scientiarum Mathematicarum Hungarica,2001,37(1):69-81.