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

María Inés Gareis, Federico Dario Kovac and Fabián Eduardo Levis

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3328-3343

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.

Date: 2023
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https://doi.org/10.1002/mana.202200099

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