Skip to main content
SpringerLink
Log in

Superadditivity of the Levinson functional and applications

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We study the Levinson functional, constructed as a difference between the right-hand side and the left-hand side of the Levinson inequality. We show that it possesses the properties of superadditivity and monotonicity. As a consequence, we obtain mutual bounds for this functional, expressed via the non-weighted functional of the same type. In this way, a refinement and a converse of the Levinson inequality in a difference form is obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I.A. Baloch, J. Pečarić, M. Praljak, Generalization of Levinson’s inequality. J. Math. Inequal. 9, 571–586 (2015)

    Article  MathSciNet  Google Scholar 

  2. P.S. Bullen, An inequality of N. Levinson. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 421–460, 109–112 (1973)

    MathSciNet  Google Scholar 

  3. V. Čuljak, B. Ivanković, J. Pečarić, On Jensen-McShane’s inequality. Period. Math. Hung. 58(2), 139–154 (2009)

    Article  MATH  Google Scholar 

  4. S.S. Dragomir, J.E. Pečarić, L.E. Persson, Properties of some functionals related to Jensen’s inequality. Acta Math. Hung. 70(1–2), 129–143 (1996)

    Article  MATH  Google Scholar 

  5. M. Krnić, N. Lovričević, J. Pečarić, Jessen’s functional, its properties and applications. An. Şt. Univ. Ovidius Constanţa 20, 225–248 (2012)

    MATH  Google Scholar 

  6. M. Krnić, N. Lovričević, J. Pečarić, On the properties of McShane’s functional and their applications. Period. Math. Hung. 66(2), 159–180 (2013)

    Article  MATH  Google Scholar 

  7. N. Levinson, Generalization of an inequality of Ky Fan. J. Math. Anal. Appl. 8, 133–134 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  8. A.M. Mercer, Short proof of Jensen’s and Levinson’s inequalities. Math. Gaz. 94, 492–495 (2010)

    Google Scholar 

  9. D.S. Mitrinović, J.E. Pečarić, A.M. Fink, Classical and new inequalities in analysis (Kluwer Academic Publishers, Dordrecht, 1993)

    Book  MATH  Google Scholar 

  10. J. Pečarić, M. Praljak, A. Witkowski, Generalized Levinson’s inequality and exponential convexity. Opusc. Math. 35(3), 397–410 (2015)

    Article  Google Scholar 

  11. J.E. Pečarić, F. Proschan, Y.L. Tong, Convex functions, partial orderings and statistical applications (Academic Press, Inc., Boston, 1992)

    MATH  Google Scholar 

  12. T. Popoviciu, Sur une inealite de N. Levinson. Mathematica (Cluj) 6, 301–306 (1964)

    MathSciNet  Google Scholar 

  13. A. Witkowski, On Levinson’s inequality. RGMIA research report collection 15 (2012), Article 68

Download references

Acknowledgments

The research of the authors has been fully supported by Croatian Science Foundation under the project 5435.

Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

  2. Faculty of Civil Engineering and Architecture, University of Split, Matice hrvatske 15, 21000, Split, Croatia

    Neda Lovričević

  3. Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia

    Josip Pečarić

Authors
  1. Mario Krnić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neda Lovričević
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Josip Pečarić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Krnić.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krnić, M., Lovričević, N. & Pečarić, J. Superadditivity of the Levinson functional and applications. Period Math Hung 71, 166–178 (2015). https://doi.org/10.1007/s10998-015-0090-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-015-0090-3

Keywords

Mathematics Subject Classification

Search

Navigation