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Abstract <p> We show that the results of a recently published paper are incorrect. Also we introduce a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1135_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> </InlineEquation>-functional for functions define on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1135_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb R_+\)</EquationSource> </InlineEquation> and prove direct and inverse approximation theorems connecting the best approximations by special subspaces of piecewise constant functions and this <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1135_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> </InlineEquation>-functiona </p>

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On a Recent Paper Devoted to Jackson-Type Inequalities and Walsh-Fourier Transform

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • S. S. Volosivets

摘要

Abstract

We show that the results of a recently published paper are incorrect. Also we introduce a \(K\) -functional for functions define on \(\mathbb R_+\) and prove direct and inverse approximation theorems connecting the best approximations by special subspaces of piecewise constant functions and this \(K\) -functiona