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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

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Online
ISSN
2391-5455
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Volume 13, Issue 1

Issues

Inequality for power series with nonnegative coefficients and applications

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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-19 | DOI: https://doi.org/10.1515/math-2015-0061

Abstract

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.

Keywords: Jensen’s inequality; Measurable functions; Lebesgue integral; Selfadjoint operators; Functions of selfadjoint operators

References

  • [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. Web of ScienceCrossrefGoogle Scholar

  • [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. Google Scholar

  • [3] Cheng X.-L., Sun J., Note on the perturbed trapezoid inequality, J. Inequal. Pure & Appl. Math., 3(2) (2002), Art. 21. Google Scholar

  • [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]. Google Scholar

  • [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. CrossrefGoogle Scholar

  • [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]. CrossrefGoogle Scholar

  • [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]. Google Scholar

  • [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]. Google Scholar

  • [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. Google Scholar

  • [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 Google Scholar

  • [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 Google Scholar

  • [12] Helmberg G., Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc. -New York, 1969. Google Scholar

  • [13] Jensen J. L. W. V., Sur les fonctions convexes et les inegalités entre les valeurs moyennes, Acta Math., 30 (1906), 175-193. CrossrefGoogle Scholar

About the article

Received: 2015-07-20

Accepted: 2015-09-10

Published Online: 2015-10-19


Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0061.

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©2015 Silvestru Sever Dragomir. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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