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

Abstract

In this paper, we consider the best polynomial approximation operator defined on an Orlicz–Lorentz space (Figure presented.), and its extension to (Figure presented.), where w is a non-negative continuous weight function and (Figure presented.) 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.