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**Extension of Jensen’s inequality for operators without operator convexity.**
*(English)*
Zbl 1221.47032

Summary: We give an extension of Jensen’s inequality for \(n\)-tuples of selfadjoint operators, unital \(n\)-tuples of positive linear mappings, and real-valued continuous convex functions with conditions on the operators’ bounds. We also study operator quasiarithmetic means under the same conditions.

### MSC:

47A63 | Linear operator inequalities |

47A64 | Operator means involving linear operators, shorted linear operators, etc. |

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\textit{J. Mićić} et al., Abstr. Appl. Anal. 2011, Article ID 358981, 14 p. (2011; Zbl 1221.47032)

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### References:

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[2] | F. Hansen, J. Pe, and I. Perić, “Jensen’s operator inequality and its converses,” Mathematica Scandinavica, vol. 100, no. 1, pp. 61-73, 2007. · Zbl 1151.47025 |

[3] | J. Mićić, J. Pe, and Y. Seo, “Converses of Jensen’s operator inequality,” Operators and Matrices, vol. 4, no. 3, pp. 385-403, 2010. · Zbl 1239.47016 |

[4] | J. Mićić, Z. Pavić, and J. Pe, “Jensen’s inequality for operators without operator convexity,” Linear Algebra and its Applications, vol. 434, no. 5, pp. 1228-1237, 2011. · Zbl 1216.47026 · doi:10.1016/j.laa.2010.11.004 |

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