AIMS Mathematics, 2020, 5(4): 3357-3364. doi: 10.3934/math.2020216

Research article

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

On inequalities of Bellman and Aczél type

Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

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.
  Article Metrics


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.    

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.    

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.    

8. M. Lin, The Hua matrix and inequalities related to contractive matrices, Linear Algebra Appl., 511 (2016), 22-30.    

9. J. T. Liu, Y. T. Poon, Q. W. Wang, A generalized Hölder type eigenvalue inequality, Linear Multilinear Algebra, 65 (2017), 2145-2151.    

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.    

12. M. S. Moslehian, Operator Aczél inequality, Linear Algebra Appl., 434 (2011), 1981-1987.    

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.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved