Pointwise approximation of functions by matrix operators of their Fourier series with $r$- differences of the entries

TL;DR

This paper extends previous Fourier series approximation results by incorporating r-differences of matrix entries, providing a more general framework for function approximation using matrix operators.

Contribution

It introduces a generalized approach to Fourier series approximation by utilizing r-differences of matrix entries, expanding upon prior results in the field.

Findings

Extended approximation estimates involving r-differences.

Generalized framework for matrix operator-based Fourier approximation.

Improved bounds for function approximation errors.

Abstract

We extend the results of Xh. Z. Krasniqi [Acta Comment. Univ. Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24]. to the case where in the measures of estimations there are used $r$-differences of the entries.