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
[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. |