On n-K Width of Certain Function Classes Defined by Linear Operators in L2 Space

YU Rui-fang, WU Ga-ridi

doi:10.13371/j.cnki.chin.q.j.m.2016.01.012

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 1: 96 - 101

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.01.012

On n-K Width of Certain Function Classes Defined by Linear Operators in L₂ Space

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Department of Mathematics, Inner Mongolia Normal University

YU Rui-fang(1991-), female(Meng), native of Chifeng, Inner Mongolia, postgraduate, engages in function approximation theory; WU Ga-ridi(1962-), male(Meng), native of Tongliao, Inner Mongolia, Master Instructor, a professors of Inner Mongolia Normal University, engages in function approximation theory.

Received date: 2015-06-25

Online published: 2020-11-18

Supported by

Supported by the National Natural Science Foundation of China(11161033)； Supported by the Inner Mongolia Normal University Talent Project Foundation（RCPY-2-2012-K-036）;Supported by the Inner Mongolia Normal University Graduate Research Innovation Foundation（CXJJS14053）； Supported by the Inner Mongolia Autonomous Region Graduate Research Innovation Foundation(S20141013525)；

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Abstract

Let M（u） be an N-function, L_r（f, x） and K_r（f, x） are Bak operator and Kantorovich operator, W_M（L_r（f）） and W_M（K_r（f）） are the Sobolev-Orlicz classes defined by L_r（f, x）, K_r（f, x） and M（u）. In this paper we give the asymptotic estimates of the n-K widths d_n（W_M（L_r（f））, L₂[0, 1]） and d_n（W_M（K_r（f））, L₂[0, 1]）.

Key words： linear operator; Sobolev-Orlicz class; width

Cite this article

YU Rui-fang, WU Ga-ridi . On n-K Width of Certain Function Classes Defined by Linear Operators in L₂ Space[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(1) : 96 -101 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.01.012

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