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On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces

Author

Listed:
  • Ling-Xiong Han

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

  • Feng Qi

    (Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
    School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

Abstract

In this paper, the authors introduce the Orlicz spaces corresponding to the Young function and, by virtue of the equivalent theorem between the modified K -functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for linear combinations of modified summation operators of integral type in the Orlicz spaces.

Suggested Citation

  • Ling-Xiong Han & Feng Qi, 2018. "On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces," Mathematics, MDPI, vol. 7(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:6-:d:192319
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    References listed on IDEAS

    as
    1. Danilo Costarelli & Gianluca Vinti, 2017. "Convergence for a family of neural network operators in Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(2-3), pages 226-235, February.
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