Aproximation of periodical function in weighted Orlicz spaces

TL;DR

This paper develops new approximation theorems for bcs-differentiable functions within weighted Orlicz spaces, expanding understanding of function approximation under Muckenhoupt weights.

Contribution

It introduces direct and inverse approximation theorems for bcs-differentiable functions in weighted Orlicz spaces with Muckenhoupt weights, a novel extension in approximation theory.

Findings

Established new direct approximation theorems.

Proved inverse approximation theorems.

Extended approximation results to weighted Orlicz spaces with Muckenhoupt weights.

Abstract

In this paper we obtained some direct and inverse theorems of approximation theory for $\psi$-differentiable functions in the metric weighted Orlicz spaces with weights, which belong to the class of Muckenhoupt.