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<p>The Milovanović–Pečarić inequality is a result of Ostrowski type. Generalizations of it, using Obreschkoff’s formula via a Fink type identity are established. Using the same approach, via a Fink type identity, the generalized trapezoidal formula and a Guessab–Schmeisser type formula are obtained. Several <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>–bounds <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((1\le p \le \infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for all considered formulas are provided.</p>

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The Obreschkoff–Ostrowski’s inequalities via Fink type identity

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Mohammad W. Alomari,
  • Gradimir V. Milovanović

摘要

The Milovanović–Pečarić inequality is a result of Ostrowski type. Generalizations of it, using Obreschkoff’s formula via a Fink type identity are established. Using the same approach, via a Fink type identity, the generalized trapezoidal formula and a Guessab–Schmeisser type formula are obtained. Several \(L^p\) L p –bounds \((1\le p \le \infty )\) ( 1 ≤ p ≤ ∞ ) for all considered formulas are provided.