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<p>Taking into consideration that the superposition of two summability methods is superior to the individual one, in this paper we present the calculations of the order of approximation of functions, conjugate to the functions belonging to weighted Lipschitz class <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(W(L^r, \Psi (u), \beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo stretchy="false">(</mo> <msup> <mi>L</mi> <mi>r</mi> </msup> <mo>,</mo> <mi mathvariant="normal">Ψ</mi> <mrow> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>; <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(r\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> by a trigonometric polynomial generated by the application of product means <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(C^{\delta }.T\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>C</mi> <mi>δ</mi> </msup> <mo>.</mo> <mi>T</mi> </mrow> </math></EquationSource> </InlineEquation> on their conjugate trigonometric Fourier series. We also derive some corollaries from our result.</p>

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Trigonometric Approximation of Functions, Conjugate to the Functions Belonging to Certain Lipschitz Spaces Using \(C^{\delta }.T\) Operator

  • 期刊论文

  • 发表日期：

    2025年1月12日

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  • Shivani Luhar,
  • Shailesh Kumar Srivastava

摘要

Taking into consideration that the superposition of two summability methods is superior to the individual one, in this paper we present the calculations of the order of approximation of functions, conjugate to the functions belonging to weighted Lipschitz class \(W(L^r, \Psi (u), \beta )\) W ( L r , Ψ ( u ) , β ) ; \(r\ge 1\) r ≥ 1 by a trigonometric polynomial generated by the application of product means \(C^{\delta }.T\) C δ . T on their conjugate trigonometric Fourier series. We also derive some corollaries from our result.