Liao, Wenshi; Wu, Junliang; Zhao, Jianguo New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant. (English) Zbl 1357.26048 Taiwanese J. Math. 19, No. 2, 467-479 (2015). Summary: We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric and geometric-harmonic mean inequalities for two positive operators. Also, new versions of reverse Young and Heinz mean inequalities for unitarily invariant norms are established. Cited in 2 ReviewsCited in 40 Documents MSC: 26D20 Other analytical inequalities 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory 26E60 Means 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Keywords:reverse Young inequalities; Kantorovich constant; operators; unitarily invariant norms PDFBibTeX XMLCite \textit{W. Liao} et al., Taiwanese J. Math. 19, No. 2, 467--479 (2015; Zbl 1357.26048) Full Text: DOI References: [1] F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361 (2010), 262-269. · Zbl 1180.15021 [2] F. Kittaneh and Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra., 59 (2011), 1031-1037. · Zbl 1225.15022 [3] F. C. Mitroi, About the precision in Jensen-Steffensen inequality, An. Univ. Craiova Ser. Mat. Inform., 37 (2010), 73-84. · Zbl 1224.26045 [4] H. Zuo, G. Shi and M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556. · Zbl 1242.47017 [5] J. M. Aldaz, Comparison of Differences between Arithmetic and Geometric Means, arXiv: 1001.5055v1. · Zbl 1244.26035 [6] J. I. Fujii, S. Izumino and Y. Seo, Determinant for positive operators and Specht’s theorem, Sci. Math., 1 (1998), 307-310. · Zbl 0991.47002 [7] J. Wu and J. Zhao, Operator inequalities and reverse inequalities related to the KittanehManasrah inequalities, Linear Multilinear Algebra., http://dx.doi.org/10.1080/03081087. 2013.794235. [8] M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), · Zbl 1021.47010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.