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Mutual bounds for Jensen-type operator inequalities related to higher order convexity

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Abstract

The main objective of this article is to establish mutual bounds for the Jensen operator inequality related to convex functions of higher order. First we give several mutual bounds for the operator version of the Lah-Ribarič inequality which hold for a class of n-convex functions. By virtue of the established estimates, we then derive several mutual bounds for the Jensen operator inequality which are also related to n-convex functions.

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References

  1. Agarwal, R.P., Wong, P.J.Y.: Error Inequalities in Polynomial Interpolation and Their Applications. Kluwer Academic Publishers, Dordrecht (1993)

    Book  Google Scholar 

  2. Bhatia, R.: Matrix Analysis. Springer, Berlin (1997)

    Book  Google Scholar 

  3. Hansen, F., Pedersen, G.: Jensen’s operator inequality. Bull. Lond. Math. Soc. 35, 553–564 (2003)

    Article  MathSciNet  Google Scholar 

  4. Hansen, F., Pečarić, J., Perić, I.: Jensen’s operator inequality and its converses. Math. Scand. 100, 61–73 (2007)

    Article  MathSciNet  Google Scholar 

  5. Jakšić, R., Krnić, M., Pečarić, J.: On some new converses of the Jensen and the Lah-Ribarič operator inequality. Hacet. J. Math. Stat. 44, 1045–1055 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Jakšić, R., Krnić, M., Pečarić, J.: More precise estimates for the Jensen operator inequality obtained via the Lah-Ribarič inequality. Appl. Math. Comput. 249, 346–355 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Krnić, M., Mikić, R., Pečarić, J.: Double precision of the Jensen-type operator inequalities for bounded and Lipschitzian functions. Aequat. Math. (2018). https://doi.org/10.1007/s00010-018-0599-7

    Article  MathSciNet  Google Scholar 

  8. Mikić, R., Pečarić, Đ., Pečarić, J.: Inequalities of the Edmundson-Lah-Ribarič Type for \(n\)-Convex Functions with Applications. arXiv:1809.08813 (Submitted for publication)

  9. Pečarić, J.E., Proschan, F., Tong, Y.L.: Convex Functions, Partial Orderings and Statistical Applications. Academic Press Inc., San Diego (1992)

    MATH  Google Scholar 

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Acknowledgements

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

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Authors and Affiliations

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

    Mario Krnić

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

    Rozarija Mikić

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

    Josip Pečarić

Authors
  1. Mario Krnić
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  2. Rozarija Mikić
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  3. Josip Pečarić
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Correspondence to Mario Krnić.

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Krnić, M., Mikić, R. & Pečarić, J. Mutual bounds for Jensen-type operator inequalities related to higher order convexity. Aequat. Math. 93, 1159–1176 (2019). https://doi.org/10.1007/s00010-018-0629-5

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  • DOI: https://doi.org/10.1007/s00010-018-0629-5

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