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.
@article{bwmeta1.element.doi-10_1515_math-2015-0061,
author = {Silvestru Sever Dragomir},
title = {Inequality for power series with nonnegative coefficients and applications},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {06576819},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0061}
}
Silvestru Sever Dragomir. Inequality for power series with nonnegative coefficients and applications. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0061/
[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] | Zbl 1198.26019
[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. | Zbl 1143.26009
[3] Cheng X.-L., Sun J., Note on the perturbed trapezoid inequality, J. Inequal. Pure & Appl. Math., 3(2) (2002), Art. 21. | Zbl 0994.26020
[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]. | Zbl 1036.26021
[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] | Zbl 1193.47023
[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] | Zbl 1280.26033
[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]. | Zbl 1275.26035
[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. | Zbl 0836.26009
[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. | Zbl 0177.42401
[13] Jensen J. L. W. V., Sur les fonctions convexes et les inegalités entre les valeurs moyennes, Acta Math., 30 (1906), 175-193. [Crossref] | Zbl 37.0422.02