On the Jensen’s inequality and its variants

Elahe Jaafari; Mohammad Sadegh Asgari; Mohsen Shah Hosseini; Baharak Moosavi; Elahe Jaafari; Mohammad Sadegh Asgari; Mohsen Shah Hosseini; Baharak Moosavi

doi:10.3934/math.2020081

AIMS Mathematics

2020, Volume 5, Issue 2: 1177-1185. doi: 10.3934/math.2020081

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Research article

On the Jensen’s inequality and its variants

1.
Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch,Tehran, Iran
2.
Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
3.
Department of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, Iran

Received: 22 October 2019 Accepted: 07 January 2020 Published: 16 January 2020
MSC : 26A51, 47A63, 26B25, 39B62, 26D15

The main purpose of this paper is to discuss operator Jensen inequality for convex functions, without appealing to operator convexity. Several variants of this inequality will be presented, and some applications will be shown too.
- Jensen’s inequality,
- convex function,
- self-adjoint operator,
- positive operator,
- positive linear map
Citation: Elahe Jaafari, Mohammad Sadegh Asgari, Mohsen Shah Hosseini, Baharak Moosavi. On the Jensen’s inequality and its variants[J]. AIMS Mathematics, 2020, 5(2): 1177-1185. doi: 10.3934/math.2020081

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Abstract

The main purpose of this paper is to discuss operator Jensen inequality for convex functions, without appealing to operator convexity. Several variants of this inequality will be presented, and some applications will be shown too.

References

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