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On a generalization of the extended best polynomial approximation operator in Orlicz–Lorentz spaces

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  • María Inés Gareis
  • Federico Dario Kovac
  • Fabián Eduardo Levis

Abstract

In this paper, we consider the best polynomial approximation operator defined on an Orlicz–Lorentz space Λw,ϕ$\Lambda _{w,\phi }$, and its extension to Λw,ϕ′$\Lambda _{w,\phi ^{\prime }}$, where w is a non‐negative continuous weight function and ϕ′$\phi ^{\prime }$ is the derivative of ϕ, which is not required to be an Orlicz function. Our work generalizes a recent result in this field on an Orlicz–Lorentz space generated by an Orlicz function. In addition, we establish some properties and estimates for any extended best polynomial approximation.

Suggested Citation

  • María Inés Gareis & Federico Dario Kovac & Fabián Eduardo Levis, 2023. "On a generalization of the extended best polynomial approximation operator in Orlicz–Lorentz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3328-3343, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3328-3343
    DOI: 10.1002/mana.202200099
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