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

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. [ABSTRACT FROM AUTHOR]