华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 2: 31 - 40

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.02.004

数学

左拟中插式Gamma算子在Orlicz空间中的逼近性质

  • 韩领兄
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  • 内蒙古民族大学 数学学院, 内蒙古 通辽 028043

收稿日期: 2017-03-22

  网络出版日期: 2018-03-22

基金资助

国家自然科学基金（11461052）；内蒙古自治区自然科学基金（2016MS0118）；内蒙古民族大学科学研究项目（NMDYB15087）

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Approximation properties of the left quasi-interpolants Gamma operators in Orlicz spaces

  • HAN Ling-xiong
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  • College of Mathematics, Inner Mongolia University for the Nationalities, Tongliao Inner Mongolia 028043, China

Received date: 2017-03-22

  Online published: 2018-03-22

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摘要

为了得到更快的逼近速度，人们开始研究算子的拟中插式的逼近性质.在Orlicz空间中讨论左拟中插式Gamma算子的逼近性质，利用了Ditzian-Totik模与K-泛函的等价性、Hölder不等式、Cauchy-Schwarz不等式和Laguerre多项式等等工具得到了逼近的正、逆和等价定理，推广了左拟中插式Gamma算子在Lp空间中的逼近结果，改进了Gamma算子在Orlicz空间的逼近性质.

关键词： 左拟中插式Gamma算子; K-泛函; 连续模; 等价定理

本文引用格式

韩领兄 . 左拟中插式Gamma算子在Orlicz空间中的逼近性质[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(2) : 31 -40 . DOI: 10.3969/j.issn.1000-5641.2018.02.004

Abstract

In order to reach better approximation degree, people start to study the quasiinterpolants of operators. In this paper, approximation properties of left quasi-interpolants Gamma operators are discussed by the tools of Ditizan-Totik modulus, K-functional, Hölder's inequality, Cauchy-Schwarz's inequality and Laguerre polynomials and so on. Then we obtain the direct, inverse and equivalence theorems which generalize the results of left quasi-interpolants Gamma operators in Lp space and improve the approximation properties of Gamma operators in Orlicz spaces.

Key words： left quasi-interpolants Gamma operator; K-functional; modulus of smoothness; equivalence theorem

参考文献

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