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<p>The purpose of this paper is to utilize Abel-Gontscharoff and Hermite interpolation polynomials to prove new bounds for identities related to generalizations of Steffensen’s inequality. This will be achieved through the use of the weighted Hermite–Hadamard-type inequality utilizing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((n+2)-\)</EquationSource> </InlineEquation>convex functions.</p>

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New bounds for identities related to generalizations of Steffensen’s inequality via Abel-Gontscharoff’s and Hermite’s interpolation polynomials

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Josip Pečarić,
  • Anamarija Perušić Pribanić,
  • Ksenija Smoljak Kalamir

摘要

The purpose of this paper is to utilize Abel-Gontscharoff and Hermite interpolation polynomials to prove new bounds for identities related to generalizations of Steffensen’s inequality. This will be achieved through the use of the weighted Hermite–Hadamard-type inequality utilizing \((n+2)-\) convex functions.