Research article

On inequalities of Bellman and Aczél type

  • Received: 06 October 2019 Accepted: 23 March 2020 Published: 31 March 2020
  • MSC : 15A42, 15A60, 47A30

  • The purpose of this paper is to prove some eigenvalue inequalities involving convex functions. These extend many remarkable inequalities, most of them related to the Bellman and Aczél inequalities.

    Citation: Mohsen Erfanian Omidvar, Hamid Reza Moradi. On inequalities of Bellman and Aczél type[J]. AIMS Mathematics, 2020, 5(4): 3357-3364. doi: 10.3934/math.2020216

    Related Papers:

  • The purpose of this paper is to prove some eigenvalue inequalities involving convex functions. These extend many remarkable inequalities, most of them related to the Bellman and Aczél inequalities.


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    [1] J. Aczél, Some general methods in the theory of functional equations in one variable. New applications of functional equations, Uspehi Mat. Nauk (N.S.), 11 (1956), 3-68.
    [2] J. S. Aujla, F. C. Silva, Weak majorization inequalities and convex functions, Linear Algebra Appl., 369 (2003), 217-233. doi: 10.1016/S0024-3795(02)00720-6
    [3] R. Bellman, On an inequality concerning an indefinite form, Amer. Math. Monthly., 63 (1956), 101-109.
    [4] R. Bhatia, Matrix Analysis, Springer Verlag, New York, 1997.
    [5] J. C. Bourin, E. Y. Lee, M. Fujii, et al. A matrix reverse Hölder inequality, Linear Algebra Appl., 431 (2009), 2154-2159. doi: 10.1016/j.laa.2009.07.010
    [6] T. Furuta, J. Mićić-Hot, J. Pečarić, et al. Mond-Pečarić Method in Operator Inequalities, Element, Zagreb, 2005.
    [7] E. Jaafari, M. S. Asgari, M. Shah Hosseini, et al. On the Jensen's inequality and its variants, AIMS Mathematics., 5 (2020), 1177-1185. doi: 10.3934/math.2020081
    [8] M. Lin, The Hua matrix and inequalities related to contractive matrices, Linear Algebra Appl., 511 (2016), 22-30. doi: 10.1016/j.laa.2016.09.003
    [9] J. T. Liu, Y. T. Poon, Q. W. Wang, A generalized Hölder type eigenvalue inequality, Linear Multilinear Algebra, 65 (2017), 2145-2151. doi: 10.1080/03081087.2017.1338244
    [10] H. R. Moradi, M. Sababheh, Eigenvalue inequalities for n-tuple of matrices, Linear Multilinear Algebra, (2019), 1-12.
    [11] A. Morassaei, F. Mirzapour, M. S. Moslehian, Bellman inequality for Hilbert space operators, Linear Algebra Appl., 438 (2013), 3776-3780. doi: 10.1016/j.laa.2011.06.042
    [12] M. S. Moslehian, Operator Aczél inequality, Linear Algebra Appl., 434 (2011), 1981-1987. doi: 10.1016/j.laa.2010.11.043
    [13] S. Sheybani, M. E. Omidvar, H. R. Moradi, New inequalities for operator concave functions involving positive linear maps, Math. Inequal. Appl., 21 (2018), 1167-1174.
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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