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2015 | 13 | 1 |
Tytuł artykułu

Inequality for power series with nonnegative coefficients and applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-07-20
zaakceptowano
2015-09-10
online
2015-10-19
Twórcy
  • Mathematics, School 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] Agarwal R. P., Dragomir S. S., A survey of Jensen type inequalities for functions of selfadjoint operators in Hilbert spaces.Comput. Math. Appl. 59 (2010), no. 12, 3785–3812.[WoS][Crossref]
  • [2] Cerone P., Dragomir S. S., A refinement of the Grüss inequality and applications, Tamkang J. Math. 38 (2007), No. 1, 37-49.Preprint RGMIA Res. Rep. Coll., 5 (2) (2002), Art. 14.
  • [3] Cheng X.-L., Sun J., Note on the perturbed trapezoid inequality, J. Inequal. Pure & Appl. Math., 3(2) (2002), Art. 21.
  • [4] Dragomir S. S., A Grüss type inequality for isotonic linear functionals and applications. Demonstratio Math. 36 (2003), no. 3, 551–562. Preprint RGMIA Res. Rep. Coll. 5(2002), Suplement, Art. 12. [Online http://rgmia.org/v5(E).php].
  • [5] Dragomir S. S., Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces. J. Inequal. Appl.2010, Art. ID 496821, 15 pp.[Crossref]
  • [6] Dragomir S. S., Reverses of the Jensen inequality in terms of the first derivative and applications, Acta Math. Vietnam. 38 (2013),no. 3, 429–446. Preprint RGMIA Res. Rep. Coll. 14 (2011), Art. 71. [http://rgmia.org/papers/v14/v14a71.pdf].[Crossref]
  • [7] Dragomir S. S., Some reverses of the Jensen inequality with applications, Bull. Aust. Math. Soc. 87 (2013), no. 2, 177–194.Preprint RGMIA Res. Rep. Coll. 14 (2011), Art. 72. [http://rgmia.org/papers/v14/v14a72.pdf].
  • [8] Dragomir S. S., A refinement and a divided difference reverse of Jensen’s inequality with applications, Preprint RGMIA Res. Rep.Coll. 14 (2011), Art. 74. [http://rgmia.org/papers/v14/v14a74.pdf].
  • [9] Dragomir S. S., Ionescu N. M., Some converse of Jensen’s inequality and applications. Rev. Anal. Numér. Théor. Approx. 23(1994), no. 1, 71–78.
  • [10] Dragomir S. S., Operator Inequalities of the Jensen, Cˇ ebyšev and Grüss Type. Springer Briefs in Mathematics. Springer, NewYork, 2012. xii+121 pp. ISBN: 978-1-4614-1520-6
  • [11] Dragomir S. S., Operator Inequalities of Ostrowski and Trapezoidal Type. Springer Briefs in Mathematics. Springer, New York,2012. x+112 pp. ISBN: 978-1-4614-1778-1
  • [12] Helmberg G., Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc. -New York, 1969.
  • [13] Jensen J. L. W. V., Sur les fonctions convexes et les inegalités entre les valeurs moyennes, Acta Math., 30 (1906), 175-193.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0061
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