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On Willett’s, Godunova-Levin’s, and Rozanova’s Opial-type inequalities with related Stolarsky-type means

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Abstract

In this paper, we consider generalizations of Opial’s inequality due to Willett, Godunova, Levin, and Rozanova. Cauchy-type mean-value theorems are proved and used in studying Stolarsky-type means defined by the obtained inequalities. Also, a method of producing n-exponentially convex and exponentially convex functions is applied.

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Authors and Affiliations

  1. University of Split, Split, Croatia

    M. Andrić & A. Barbir

  2. University of Zagreb, Zagreb, Croatia

    J. Pečarić

Authors
  1. M. Andrić
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  2. A. Barbir
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  3. J. Pečarić
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Corresponding author

Correspondence to M. Andrić.

Additional information

Published in Russian in Matematicheskie Zametki, 2014, Vol. 96, No. 6, pp. 803–819.

The text was submitted by the authors in English.

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Andrić, M., Barbir, A. & Pečarić, J. On Willett’s, Godunova-Levin’s, and Rozanova’s Opial-type inequalities with related Stolarsky-type means. Math Notes 96, 841–854 (2014). https://doi.org/10.1134/S0001434614110212

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  • DOI: https://doi.org/10.1134/S0001434614110212

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