Upper and lower bounds for the difference between the weighted arithmetic and harmonic operator means
doi:10.17398/2605-5686.34.1.41
Palabras clave:
Young’s inequality, convex functions, arithmetic mean-Harmonic mean inequality, operator means, operator inequalitiesResumen
In this paper we establish some new upper and lower bounds for the difference between the weighted arithmetic and harmonic operator means under various assumption for the positive invertible operators A, B. Some applications when A, B are bounded above and below by positive constants are given as well.
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Referencias
S.S. Dragomir, Bounds for the normalised Jensen functional, Bull. Austral. Math. Soc. 74 (3) (2006), 417 – 478.
S.S. Dragomir, A note on Young’s inequality, preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 126, http://rgmia.org/papers/v18/v18a126.pdf.
S.S. Dragomir, Some new reverses of Young’s operator inequality, preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 130, http://rgmia.org/papers/v18/v18a130.pdf.
S.S. Dragomir, On new refinements and reverses of Young’s operator inequality, preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 135, http://rgmia.org/papers/v18/v18a135.pdf.
S.S. Dragomir, Some inequalities for operator weighted geometric mean, preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 139, http://rgmia.org/papers/v18/v18a139.pdf.
S.S. Dragomir, Some reverses and a refinement of Hölder operator inequality, preprint RGMIA Res. Rep. Coll. 18 (2015), Art. 147, http://rgmia.org/papers/v18/v18a147.pdf.
S.S. Dragomir, Some inequalities for weighted harmonic and arithmetic operator means, preprint RGMIA Res. Rep. Coll. 19 (2016), Art. 5, http://rgmia.org/papers/v19/v19a05.pdf.
S. Furuichi, Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc. 20 (2012), 46 – 49.
S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21 – 31.
W. Liao, J. Wu, J. Zhao, New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math. 19 (2) (2015), 467 – 479.
M. Tominaga, Specht’s ratio in the Young inequality, Sci. Math. Japon. 55 (2002), 583 – 588.
G. Zuo, G. Shi, M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal. 5 (2011), 551 – 556.
