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On the Jensen-Steffensen inequality for generalized convex functions

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Abstract

Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Natural Sciences, Mathematics and Education, University of Split, Teslina 12, 21000, Split, Croatia

    M. Klaričić Bakula

  2. Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Rudera Boškovića b.b., 21000, Split, Croatia

    A. Matković

  3. Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 30, 10000, Zagreb, Croatia

    J. Pečarić

Authors
  1. M. Klaričić Bakula
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  2. A. Matković
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  3. J. Pečarić
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Correspondence to M. Klaričić Bakula.

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Communicated by László Hatvani

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Bakula, M.K., Matković, A. & Pečarić, J. On the Jensen-Steffensen inequality for generalized convex functions. Period Math Hung 55, 19–34 (2007). https://doi.org/10.1007/s10998-007-3019-x

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  • DOI: https://doi.org/10.1007/s10998-007-3019-x

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