On the degree of approximation of continuous functions by a linear transformation of their Fourier series

TL;DR

This paper investigates how well continuous functions can be approximated using matrix means of their Fourier series, providing theoretical bounds based on the functions' modulus of continuity.

Contribution

It introduces four new theorems that quantify the approximation degree of continuous functions via matrix means of Fourier series, expanding understanding of Fourier approximation methods.

Findings

Four new theorems on approximation bounds

Approximation expressed in terms of modulus of continuity

Results applicable to matrix means of Fourier series

Abstract

In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.