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**Inequalities of convex functions and self-adjoint operators.**
*(English)*
Zbl 1300.47025

Summary: The paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic operator mean inequality is derived as an example.

### MSC:

47A63 | Linear operator inequalities |

39B62 | Functional inequalities, including subadditivity, convexity, etc. |

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\textit{Z. Pavić}, J. Oper. 2014, Article ID 382364, 5 p. (2014; Zbl 1300.47025)

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### References:

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[10] | J. Mićić, Z. Pavić, and J. Pe, “The inequalities for quasiarithmetic means,” Abstract and Applied Analysis, vol. 2012, Article ID 203145, 25 pages, 2012. · Zbl 1246.26019 |

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