Research article

On the Jensen’s inequality and its variants

  • 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.

    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

    Related Papers:

  • 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.


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    [2] M. D. Choi, A. Schwarz, Inequality for positive linear maps on C*-algebras, Illinois J. Math., 18 (1974), 565-574. doi: 10.1215/ijm/1256051007
    [3] S. Furuichi, H. R. Moradi, A. Zardadi, Some new Karamata type inequalities and their applications to some entropies, Rep. Math. Phys., 84 (2019), 201-214. doi: 10.1016/S0034-4877(19)30083-7
    [4] F. Hansen, J. Pečarić, J. Perić, Jensen's operator inequality and it's converses, Math. Scand., 100 (2007), 61-73. doi: 10.7146/math.scand.a-15016
    [5] L. Horváth, K. A. Khan, J. Pečarić, Cyclic refinements of the different versions of operator Jensen's inequality, Electron. J. Linear Algebra, 31 (2016), 125-133. doi: 10.13001/1081-3810.3098
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    [7] J. S. Matharu, M. S. Moslehian, J. S. Aujla, Eigenvalue extensions of Bohr's inequality, Linear Algebra Appl., 435 (2011), 270-276. doi: 10.1016/j.laa.2011.01.023
    [8] A. McD. Mercer, A variant of Jensen's inequality, J. Inequal. Pure Appl. Math., 4 (2003), 73.
    [9] J. Mićić, H. R. Moradi, S. Furuichi, Choi-Davis-Jensen's inequality without convexity, J. Math. Inequal., 12 (2018), 1075-1085.
    [10] B. Mond, J. Pečarić, On Jensen's inequality for operator convex functions, Houston J. Math., 21 (1995), 739-753.
    [11] H. R. Moradi, S. Furuichi, F. C. Mitroi-Symeonidis, An extension of Jensen's operator inequality and its application to Young inequality, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 113 (2019), 605-614.
    [12] H. R. Moradi, M. E. Omidvar, M. Adil Khan, Around Jensen's inequality for strongly convex functions, Aequationes Math., 92 (2018), 25-37. doi: 10.1007/s00010-017-0496-5
    [13] M. Sababheh, H. R. Moradi, S. Furuichi, Integrals refining convex inequalities, Bull. Malays. Math. Sci. Soc., 2019 (2019), 1-17.
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