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

  • Mario KrnićEmail author
  • Rozarija Mikić
  • Josip Pečarić
Article
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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.

Keywords

Jensen operator inequality Lah-Ribarič operator inequality n-Convexity Mutual bounds 

Mathematics Subject Classification

Primary 47A63 Secondary 26A51 

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Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mario Krnić
    • 1
    Email author
  • Rozarija Mikić
    • 2
  • Josip Pečarić
    • 3
  1. 1.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia
  2. 2.Faculty of Textile TechnologyUniversity of ZagrebZagrebCroatia
  3. 3.RUDN UniversityMoscowRussia

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