左拟中插式Gamma算子在Orlicz空间中的逼近性质

doi:10.3969/j.issn.1000-5641.2018.02.004

华东师范大学学报(自然科学版) ›› 2018, Vol. 2018 ›› Issue (2): 31-40.doi: 10.3969/j.issn.1000-5641.2018.02.004

左拟中插式Gamma算子在Orlicz空间中的逼近性质

韩领兄

内蒙古民族大学数学学院, 内蒙古通辽 028043

收稿日期:2017-03-22 出版日期:2018-03-25 发布日期:2018-03-22
通讯作者: 韩领兄,女,副教授,研究方向为函数逼近论.E-mail:hlx2980@163.com. E-mail:hlx2980@163.com
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）

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

HAN Ling-xiong

College of Mathematics, Inner Mongolia University for the Nationalities, Tongliao Inner Mongolia 028043, China

Received:2017-03-22 Online:2018-03-25 Published:2018-03-22

摘要/Abstract

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L_p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

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 L_p 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

中图分类号:

O174.41

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.

HAN Ling-xiong. Approximation properties of the left quasi-interpolants Gamma operators in Orlicz spaces[J]. Journal of East China Normal University(Natural Sc, 2018, 2018(2): 31-40.

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左拟中插式Gamma算子在Orlicz空间中的逼近性质

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

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