Some inequalities for weighted harmonic and arithmetic operator means

• Autorzy: Dragomir S. S.

Identyfikatory

DOI

10.1515/fascmath-2018-0016

• Języki publikacji: EN

Abstrakty

EN

In this paper we establish some upper and lower bounds for the difference between the weighted arithmetic and harmonie 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.

Słowa kluczowe

EN

Young’s inequality; convex functions; arithmetic mean-harmonic mean inequality; operator means; operator inequalities

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 61
• Strony: 43--54
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Dragomir S. S.

• Mathematics, College of Engineering & Science Victoria University, Po Box 14428 Melbourne City, Mc 8001, Australia and School of Computer Science & Applied Mathematics University of the Witwatersrand Private Bag 3, Johannesburg 2050, South Africa

Bibliografia

• [1] Dragomir S.S., A note on Young’s inequality, Rev. R. Acad Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 111(2)(2017), 349-354, Preprint RGMIA Res. Rep. Coll., 18(2015), Art. 126., http://rgmia.org/papers/v18/v18a126.pdf.
• [2] Dragomir S.S., Some new reverses of Young’s operator inequality, Preprint RGMIA Res. Rep. Coll., 18(2015), Art. 130, http://rgmia.org/papers/v18/v18a130.pdf.
• [3] Dragomir S.S., 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.
• [4] Dragomir S.S., Some inequalities for operator weighted geometric mean, Preprint RGMIA Res. Rep. Coll., 18(2015), Art. 139, http://rgmia.org/papers/v18/v18a139.pdf.
• [5] Dragomir S.S., 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.
• [6] Dragomir S.S., Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74(3)(2006), 417-478.
• [7] Furuichi S., Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc., 20(2012), 46-49.
• [8] Furuichi S., On refined Young inequalities and reverse inequalities, J. Math. Inequal., 5(2011), 21-31.
• [9] Liao W., Wu J., Zhao J., New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math., 19(2)(2015), 467-479.
• [10] Zuo G., Shi G., Fujii M., Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5(2011), 551-556.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).