数学季刊 ›› 2024, Vol. 39 ›› Issue (4): 399-406.doi: 10.13371/j.cnki.chin.q.j.m.2024.04.006

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(E,q)(C,α,β) 平均在Orlicz空间内的逼近阶

  

  1. 1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China; 2. Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application, Inner Mongolia, Hohhot 010022, China; 3. Center for Applied Mathematical Science, Inner Mongolia, Hohhot 010022, China
  • 收稿日期:2024-06-20 出版日期:2024-12-30 发布日期:2024-12-30
  • 通讯作者: WU Ga-ridi (1962-), male, native of Tongliao, Inner Mongolia, professor of Inner Mongolia Normal University, Doctoral supervisor, engages in approximation theory of functions. E-mail:wgrd@imnu.edu.cn
  • 作者简介:CHEN Lin (1999-), female, native of Ulanqab, Inner Mongolia, postgraduate of Inner Mongolia Normal University, engages in approximation theory of functions; WU Ga-ridi (1962-), male, native of Tongliao, Inner Mongolia, professor of Inner Mongolia Normal University, Doctoral supervisor, engages in approximation theory of functions.
  • 基金资助:
    Supported by the National Natural Science Foundation of China (Grant No. 11761055); The Fundamental Research Funds for the Inner Mongolia Normal University (Grant No. 2023JBZD007); The First-Class Disciplines Project, Inner Mongolia Autonomous Region (Grant No. YLXKZX-NSD-001); Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414).

The Degree of Approximation by (E,q)(C,α,β) Means in Orlicz Spaces

  1. 1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China; 2. Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application, Inner Mongolia, Hohhot 010022, China; 3. Center for Applied Mathematical Science, Inner Mongolia, Hohhot 010022, China
  • Received:2024-06-20 Online:2024-12-30 Published:2024-12-30
  • Contact: WU Ga-ridi (1962-), male, native of Tongliao, Inner Mongolia, professor of Inner Mongolia Normal University, Doctoral supervisor, engages in approximation theory of functions. E-mail:wgrd@imnu.edu.cn
  • About author:CHEN Lin (1999-), female, native of Ulanqab, Inner Mongolia, postgraduate of Inner Mongolia Normal University, engages in approximation theory of functions; WU Ga-ridi (1962-), male, native of Tongliao, Inner Mongolia, professor of Inner Mongolia Normal University, Doctoral supervisor, engages in approximation theory of functions.
  • Supported by:
    Supported by the National Natural Science Foundation of China (Grant No. 11761055); The Fundamental Research Funds for the Inner Mongolia Normal University (Grant No. 2023JBZD007); The First-Class Disciplines Project, Inner Mongolia Autonomous Region (Grant No. YLXKZX-NSD-001); Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414).

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摘要： In this paper, we study the trigonometric approximation problems of functions which belong to the Lipα class, the Lip(ξ(t)) class, and the W(L∗M;ξ(t)) class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces, the second mean value theorem for integrals, and (E,q)(C,α,β) means etc. At the same time, we give the corresponding degree of approximation.

关键词: Orlice space, Trigonometric approximation, Degree of approximation

Abstract: In this paper, we study the trigonometric approximation problems of functions which belong to the Lipα class, the Lip(ξ(t)) class, and the W(L∗M;ξ(t)) class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces, the second mean value theorem for integrals, and (E,q)(C,α,β) means etc. At the same time, we give the corresponding degree of approximation.

Key words: Orlice space, Trigonometric approximation, Degree of approximation

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