Some reverses of Hölder vector operator inequality

• Autorzy: Dragomir, S. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain some new reverses of Hölder vector inequality for positive operators on Hilbert spaces.

Słowa kluczowe

EN

Young’s inequality; Hölder operator inequality; arithmetic mean-geometric mean inequality

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2019
• Tom: nr 62
• Strony: 35--46
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Dragomir, S. S.

• Mathematics, College of Engineering & Science Victoria University, Po Box 14428 Melbourne City, MC 8001, Australia,
• 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, Preprint RGMIA Res. Rep. Coll., 18(2015), Art. 126. [http://rgmia.org/papers/v18/v18a126.pdf].
• [2] Dragomir S.S., A note on new refinements and reverses of Young’s inequality, Preprint RGMIA Res. Rep. Coll., 18(2015). [http://rgmia.org/ papers/v1].
• [3] Dragomir S.S., Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces, J. Inequal. & Appl., Vol. 2010, Article ID 496821, 15 pages doi:10.1155/2010/496821Preprint RGMIA Res. Rep. Coll., 11(2008), Supliment. Art. 15. [Online http://rgmia.org /papers/v11e/RevJensenOp.pdf].
• [4] Dragomir S.S., Operator Inequalities of the Jensen, Čebyšev and Grüss Type, Springer Briefs in Mathematics, Springer, 2012.
• [5] Fujii M., Izumino S., Nakamoto R., Classes of operators determined by the Heinz-Kato-Furuta inequality and the Hölder-McCarthy inequality, Nihonkai Math. J., 5(1)(1994), 61-67.
• [6] Fuji M., Izumino S., Nakamoto R., Seo Y., Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities, Nihonkai Math. J, 8(1997), 117-122.
• [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] Furuichi S., Minculete N., Alternative reverse inequalities for Young’s inequality, J. Math Ineąual., 5(4)(2011), 595-600.
• [10] Furuta T., Extensions of Hölder-McCarthy and Kantorovich inequalities and their applications, Proc. Japan Acad. Ser. A Math. Sci., 73(3)(1997), 38-41.
• [11] Furuta T., Operator inequalities associated with Hölder-McCarthy and Kantorovich inequalities, J. Inequal. Appl., 2(2)(1998), 137-148.
• [12] Furuta T., The Hölder-McCarthy and the Young inequalities are equivalent for Hilbert space operators, Amer. Math. Monthly, 108(1)(2001), 68-69.
• [13] Greub W., Rheinboldt W., On a generalization of an inequaJity of L.V. Kantorovich, Proc. Amer. Math., 10(1959), 407-415.
• [14] Kittaneh F., Manasrah Y., Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361(2010), 262-269.
• [15] Kittaneh F., Manasrah Y., Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra, 59(2011), 1031-1037.
• [16] Lin C.-S., Cho Y.J., On Hölder-McCarthy-type inequalities with powers, J. Korean Math. Soc., 39(3)(2002), 351-361.
• [17] Lin C.-S., Cho Y.J., On Kantorovich inequality and Hölder-McCarthy inequalities, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 11(4)(2004), 481-490.
• [18] McCARTHY C.A., cp, Israel J. Math., 5(1967), 249-271.
• [19] 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.
• [20] Nakamoto R., Nakamura M., Operator mean and the Kantorovich inequality, Math. Japonica, 44(1966), 495-498.
• [21] Specht W., Zer Theorie der elementaren Mittel, Math. Z, 74(1960), 91-98.
• [22] Tominaga M., Specht’s ratio in the Young inequality, Sci. Math. Japon., 55(2002), 583-588.
• [23] 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 (2019).