Some improvements of the young mean inequality and its reverse
-
Maryam Khosravi
Abstract
The main objective of the present paper, is to obtain some new versions of Young-type inequalities with respect to two weighted arithmetic and geometric means and their reverses, using two inequalities
where r = min{ν, 1 – ν}, R = max{ν,1 – ν} and K(t,2) =
where h = max
Communicated by Werner Timmermann
References
[1] Alzer, H.—Da Fonseca, C. M.—Kovačec, A.: Young-type inequalities and their matrix analogues, Linear Multilinear Algebra 63 (2015), 622–635.10.1080/03081087.2014.891588Search in Google Scholar
[2] Bakherad, M.—Krnic, M.—Moslehian, M. S.: Reverses of the Young inequality for matrices and operators, Rocky Mountain J. Math. 46 (2016), 1089–1105.10.1216/RMJ-2016-46-4-1089Search in Google Scholar
[3] Furuichi, S.—Minculete, N.: Alternative reverse inequalities for Young’s inequality, J. Math. Inequal. 5 (2011), 595–600.10.7153/jmi-05-51Search in Google Scholar
[4] Kittaneh, F.—Manasrah, Y.: Improved Young and Heinz inequalities for matrices, J. Math. Anal. Appl. 361 (2010), 262–269.10.1016/j.jmaa.2009.08.059Search in Google Scholar
[5] Kittaneh, F.—Manasrah, Y.: Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra 59 (2011), 1031–1037.10.1080/03081087.2010.551661Search in Google Scholar
[6] Liao, W.—Wu, J.—Zhao, J.: New version of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19 (2015), 467–479.10.11650/tjm.19.2015.4548Search in Google Scholar
[7] Manjegani, S. M.—Norouzi, A.: Matrix form of the inverse Young inequality, Linear Algebra Appl. 486 (2015), 484–493.10.1016/j.laa.2015.08.022Search in Google Scholar
[8] Mitroi, F. C.: About the precision in Jensen-Steffensen inequality, An. Univ. Craiova Ser. Mat. Inform. 37 (2010), 73–84.Search in Google Scholar
[9] Pečarić, J.—Furuta, T.—Hot, J. M.—Seo, Y.: Mond-Pečarić Method in Operator Inequalities, Element, Zagreb, 2005.Search in Google Scholar
[10] Wu, J.—Zhao, J.: Operator inequalities and reverse inequalities related to the Kittaneh-Manasrah inequalities, Linear Multilinear Algebra 62 (2014), 884–894.10.1080/03081087.2013.794235Search in Google Scholar
[11] Zuo, H.—Shi, G.—Fujii, M.: Refined Young inequality with Kantorovich constant, J. Math. Inequal. 5 (2011), 551–556.10.7153/jmi-05-47Search in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
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- Some improvements of the young mean inequality and its reverse
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- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
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Articles in the same Issue
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
- Distance functions on the sets of ordinary elliptic curves in short Weierstrass form over finite fields of characteristic three
- The drazin inverse of the sum of two matrices
- Refinements of the majorization-type inequalities via green and fink identities and related results
- Characterizations and properties of graphs of Baire functions
- Some improvements of the young mean inequality and its reverse
- On characteristic of bounded analytic functions involving hyperbolic derivative
- A uniqueness problem for entire functions related to Brück’s conjecture
- System of nonlocal resonant boundary value problems involving p-Laplacian
- Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
- Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces
- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
- On generalized 4-th root metrics of isotropic scalar curvature
- Compactifications from generators and relations
- Diophantine quadruples with values in k-generalized Fibonacci numbers
