Direct and inverse approximation theorems of $2\pi$-periodic functions by Taylor--Abel--Poisson means

TL;DR

This paper establishes new direct and inverse approximation theorems for 2π-periodic functions using Taylor–Abel–Poisson operators within the integral metric, enhancing understanding of their approximation properties.

Contribution

It introduces novel approximation theorems specifically for Taylor–Abel–Poisson means in the context of 2π-periodic functions, expanding theoretical knowledge.

Findings

Established direct approximation estimates.

Proved inverse approximation theorems.

Characterized approximation quality in the integral metric.

Abstract

We obtain direct and inverse approximation theorems of $2\pi$-periodic functions by Taylor--Abel--Poisson operators in the integral metric.