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

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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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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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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Mathematics Subject Classification

  • Primary 47A63
  • Secondary 26A51

Keywords

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