Some estimates on the AM-GM inequality and its applications
محورهای موضوعی : Functional analysis
F. P. Mohebbi
1
,
M. Hassani
2
,
M. Erfanian Omidvar
3
,
H. Moradi
4
1 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
3 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
4 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
کلید واژه: Young inequality, arithmetic-geometric mean inequality, logarithmic mean,
چکیده مقاله :
The present paper seeks to establish an approximation of the arithmetic-geometric mean inequality (AM-GM) using a logarithmically concave function. We utilized the specific properties of this class of functions to derive modified versions of the AM-GM inequality as a specific example. These findings present a fresh perspective on the subject.
The present paper seeks to establish an approximation of the arithmetic-geometric mean inequality (AM-GM) using a logarithmically concave function. We utilized the specific properties of this class of functions to derive modified versions of the AM-GM inequality as a specific example. These findings present a fresh perspective on the subject.
[1] S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74 (2006), 471-478.
[2] Y. Feng, Refinements of the Heinz inequalities, J. Inequal. Appl. (2012), 2012:18.
[3] S. Furuichi, H. R. Moradi, On further refinements for Young inequalities, Open Math. 16 (1) (2018), 1478-1482.
[4] S. Furuichi, H. R. Moradi, Some refinements of classical inequalities, Rocky Mountain J. Math. 48 (7) (2018), 2289-2309.
[5] S. Furuichi, H. R. Moradi, M. Sababheh, New inequalities for interpolational operator means, J. Math. Inequal. 15 (1) (2021), 107-116.
[6] F. Kittaneh, Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl. 361 (2010), 262-269.
[7] F. Kittaneh, Y. Manasrah, Reverses Young and Heinz inequalities for matrices, Linear Multilinear Algebra. 59 (2011), 1031-1037.
[8] H. R. Moradi, M. E. Omidvar, Complementary inequalities to improved AM-GM inequality, Acta. Math. Sin. 33 (2017), 1609-1616.
[9] H. R. Moradi, M. Sababheh, S. Furuichi, On the operator Hermite-Hadamard inequality, Complex Anal. Oper. Theory. (2021), 15:122.
[10] R. Pal, M. Singh, M. S. Moslehian, J. S. Aujla, A new class of operator monotone functions via operator means, Linear Multilinear Algebra. 64 (12) (2016), 2463-2473.
[11] M. Sababheh, S. Furuichi, Z. Heydarbeygi, H. R. Moradi, On the arithmetic-geometric mean inequality, J. Math. Inequal. 15 (3) (2021), 1255-1266.
[12] M. Sababheh, H. R. Moradi, I. H. Gümü¸ s, Further inequalities for convex functions, Bull. Malays. Math. Sci. Soc. (2023), 46:42.
[13] M. Sababheh, S. Sheybani, H. R. Moradi, Matrix Fejér and Levin-Steˇ ckin inequalities, Kragujev. J. Math. 49 (5) (2025), 807-821.
[14] K. Yanagi, K. Kuriyama, S. Furuichi, Generalized Shannon inequalities based on Tsallis relative operator entropy, Linear Algebra Appl. 394 (2005), 109-118.
