| 摘要: |
| 本文在Orlicz空间中研究了Bernstein-Durrmeyer算子拟中插式Bn（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，Hölder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Bn（2r-1）（f，x）在LP空间的逼近结果. |
| 关键词: Bernstein-Durrmeyer算子 Ditzian-Totik模 正逆定理 Orlicz空间 |
| DOI： |
| 分类号:O147.41 |
| 基金项目:国家自然科学基金资助（11161033；11461052）；内蒙古自治区自然科学基金资助（2014MS0107；2016MS0118）；内蒙古民族大学科学研究项目资助（NMDYB15087）. |
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| APPROXIMATION BY BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN ORLICZ SPACES |
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HAN Ling-xiong1, WU Garidi2, GAO Hui-shuang1
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1.College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China;2.College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
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| Abstract: |
| In the present paper, we will study the approximation property of the BernsteinDurrmeyer quasi-interpolants Bn(2r-1)(f,x) in Orlicz space. By using the 2r-th Ditzian-Totik modulus of smoothness, Jensen inequality, Hölder inequality and Berens-Lorentz lemma, we obtain the direct, inverse and equivalence theorems, which generalize the approximation results of the Bernstein-Durrmeyer quasi-interpolants Bn(2r-1)(f,x) in LP space. |
| Key words: Bernstein-Durrmeyer operators Ditzian-Totik modulus direct inverse theorem Orlicz space |
