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Fejér type inequalities for higher order convex functions and quadrature formulae

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Abstract

The aim of this paper is to obtain Fejér type inequalities for higher order convex functions and the general weighted integral formula involving w-harmonic sequences of functions. Also, Fejér type inequalities are obtained for the general three, four and five point quadrature formulae. Further, Fejér type inequalities for the corrected three, corrected four and corrected five point quadrature formulae are considered. In special cases, Fejér type estimates for Simpson, Maclaurin, corrected Simpson and corrected Maclaurin quadrature rules are derived.

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Acknowledgements

The research of the third author is supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008.).

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, RuƉera Boškovića 32, 21000, Split, Croatia

    J. Barić

  2. Faculty of Science and Education, University of Mostar, Matice hrvatske bb, 88000, Mostar, Bosnia and Herzegovina

    Lj. Kvesić

  3. RUDN University, Miklukho-Maklaya str.6, Moscow, Russia, 117198

    J. Pečarić

  4. Department of Mathematics, Josip Juraj Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31000, Osijek, Croatia

    M. Ribičić Penava

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  1. J. Barić
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  2. Lj. Kvesić
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  3. J. Pečarić
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  4. M. Ribičić Penava
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All authors jointly worked on the results and they read and approved the final manuscript.

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Correspondence to M. Ribičić Penava.

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Barić, J., Kvesić, L., Pečarić, J. et al. Fejér type inequalities for higher order convex functions and quadrature formulae. Aequat. Math. 96, 417–430 (2022). https://doi.org/10.1007/s00010-021-00825-7

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  • DOI: https://doi.org/10.1007/s00010-021-00825-7

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