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<p>Some results on the degree of pointwise and normwise approximation of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40590_2025_710_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </math></EquationSource> </InlineEquation> -periodic functions by superimposing a matrix mean into a matrix mean of partial sums of their Fourier series and conjugate ones are presented under new and weaker assumptions. As the measure of estimate, some characteristics of the pointwise and normwise moduli of continuity of such functions are used. Some special cases as corollaries are also formulated.</p>

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On approximation of functions by very general matrix means of their Fourier series

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Xhevat Z. Krasniqi,
  • Włodzimierz Łenski,
  • Bogdan Szal

摘要

Some results on the degree of pointwise and normwise approximation of \(2\pi \) 2 π -periodic functions by superimposing a matrix mean into a matrix mean of partial sums of their Fourier series and conjugate ones are presented under new and weaker assumptions. As the measure of estimate, some characteristics of the pointwise and normwise moduli of continuity of such functions are used. Some special cases as corollaries are also formulated.