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More Accurate Jensen-Type Inequalities Based on the Lidstone Interpolation Formula

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Abstract

The main goal of this paper is a study of Jensen-type inequalities based on Lidstone interpolation formula. We establish Jensen-type inequalities for convex functions of even order and for completely convex functions. Besides the interpolation formula, the main results are derived by using convexity properties of the Lidstone polynomials and the corresponding Green functions. In some cases, we obtain improved variants of the basic Jensen inequality. As an application, we derive some new power mean inequalities, as well as the corresponding Hölder-type inequality. Finally, we discuss Lah–Ribarič-type inequalities for the above classes of functions. Our results are then compared with the previously known from the literature.

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Funding

The third author was partially supported through project KK.01.1.1.02.0027, a project co-financed by the Croatian Government and the European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme.

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Authors and Affiliations

  1. Department of Mathematics, Mechanical Engineering Faculty, University of Slavonski Brod, 35000, Slavonski Brod, Croatia

    Marija Bošnjak

  2. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

  3. Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Matice hrvatske 15, 21000, Split, Croatia

    Neda Lovričević

  4. Department of Mathematical, Physical and Chemical Sciences, Croatian Academy of Sciences and Arts, Zrinski trg 11, 10000, Zagreb, Croatia

    Josip Pečarić

Authors
  1. Marija Bošnjak
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  2. Mario Krnić
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  3. Neda Lovričević
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  4. Josip Pečarić
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Correspondence to Mario Krnić.

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Bošnjak, M., Krnić, M., Lovričević, N. et al. More Accurate Jensen-Type Inequalities Based on the Lidstone Interpolation Formula. Results Math 78, 247 (2023). https://doi.org/10.1007/s00025-023-02027-w

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  • DOI: https://doi.org/10.1007/s00025-023-02027-w

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