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<p>First, we introduce the generalized <i>q</i>-de la Vallée Poussin means. Then, using these new means, we extend a result of Leindler (Acta Sci Math (Szeged) 29:147–162, 1968) and one of Duman (Constr Math Anal 4(2):135–144, 2021) on uniform summability of Fourier series. In addition, we use the same means to determine the degree of approximation of a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40590_2025_715_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 function and its corresponding conjugate function in the norm of Hölder.</p>

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On generalized q-de la Vallée Poussin means

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Péter Kórus,
  • Xhevat Z. Krasniqi,
  • Bogdan Szal

摘要

First, we introduce the generalized q-de la Vallée Poussin means. Then, using these new means, we extend a result of Leindler (Acta Sci Math (Szeged) 29:147–162, 1968) and one of Duman (Constr Math Anal 4(2):135–144, 2021) on uniform summability of Fourier series. In addition, we use the same means to determine the degree of approximation of a \(2\pi \) 2 π -periodic function and its corresponding conjugate function in the norm of Hölder.