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New generalizations of Steffensen’s inequality by Lidstone’s polynomial

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Abstract

In this paper, we utilize some known Steffensen-type identities, obtained by using Lidstone’s interpolating polynomial, to prove new generalizations of Steffensen’s inequality. We obtain these new generalizations by using the weighted Hermite-Hadamard inequality for \((2n+2)-\)convex and \((2n+3)-\)convex functions. Further, the newly obtained inequalities can be observed as an upper- and lower-bound for utilized Steffensen-type identities.

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Funding

This research received no external funding.

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Authors and Affiliations

  1. Croatian Academy of Sciences and Arts, Trg Nikole Šubića Zrinskog 11, Zagreb, 10000, Croatia

    Josip Pečarić

  2. Faculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, Rijeka, 51000, Croatia

    Anamarija Perušić Pribanić

  3. Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, Zagreb, 10000, Croatia

    Ksenija Smoljak Kalamir

Authors
  1. Josip Pečarić
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  2. Anamarija Perušić Pribanić
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  3. Ksenija Smoljak Kalamir
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All authors contributed equally to the manuscript and accept its final form.

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Correspondence to Ksenija Smoljak Kalamir.

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Pečarić, J., Perušić Pribanić, A. & Smoljak Kalamir, K. New generalizations of Steffensen’s inequality by Lidstone’s polynomial. Aequat. Math. 98, 441–454 (2024). https://doi.org/10.1007/s00010-023-00953-2

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  • DOI: https://doi.org/10.1007/s00010-023-00953-2

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