Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (1): 96-101.doi: 10.13371/j.cnki.chin.q.j.m.2016.01.012

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

  

  1. Department of Mathematics, Inner Mongolia Normal University
  • Received:2015-06-25 Online:2016-03-30 Published:2020-11-18
  • About author: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.
  • 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);

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

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

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