Inequality for power series with nonnegative coefficients and applications

• Autorzy: Silvestru Sever Dragomir
• 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.

Słowa kluczowe

EN

Jensen’s inequality; Measurable functions; Lebesgue integral; Selfadjoint operators; Functions ofselfadjoint operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-07-20

zaakceptowano

2015-09-10

online

2015-10-19

Twórcy

autor

Silvestru Sever Dragomir

• 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, New York, 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]

Identyfikatory

DOI

10.1515/math-2015-0061