Skip to main content
SpringerLink
Log in

Refinements of Fejér’s inequality for convex functions

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In this paper, we establish some new refinements for the celebrated Fejér’s and Hermite-Hadamard’s integral inequalities for convex functions.

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. J. Hadamard, Étude sur les propriétés des fonctions enti`eres en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171–215.

    Google Scholar 

  2. S. S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167 (1992), 49–56.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. S. Dragomir, A refinement of Hadamard’s inequality for isotonic linear functionals, Tamkang J. Math., 24 (1993), 101–106.

    MathSciNet  MATH  Google Scholar 

  4. S. S. Dragomir, On the Hadamard’s inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775–788.

    MathSciNet  MATH  Google Scholar 

  5. S. S. Dragomir, Further properties of some mappings associated with Hermite-Hadamard inequalities, Tamkang J. Math., 34 (2003), 45–57.

    MathSciNet  MATH  Google Scholar 

  6. S. S. Dragomir, Y.-J. Cho and S.-S. Kim, Inequalities of Hadamard’s type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245 (2000), 489–501.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. S. Dragomir, D. S. Milošević and J. Sándor, On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math., 4 (1993), 3–10.

    MATH  Google Scholar 

  8. L. Fejér, Über die Fourierreihen II, Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390 (in Hungarian).

    Google Scholar 

  9. D.-Y. Hwang, K.-L. Tseng and G.-S. Yang, Some Hadamard’s inequalities for coordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11 (2007), 63–73.

    MathSciNet  MATH  Google Scholar 

  10. Z. Retkes, An extension of the Hermite-Hadamard inequality, Acta Sci. Math. (Szeged), 74 (2008), 95–106.

    MathSciNet  MATH  Google Scholar 

  11. K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, On some new inequalities of Hermite-Hadamard-Fejér type involving convex functions, Demonstratio Math., 40 (2007), 51–64.

    MathSciNet  MATH  Google Scholar 

  12. K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, Fejér-type inequalities (I), J. Inequal. Appl., 2010 (2010), Article ID 531976, 7 pages.

  13. K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, Fejér-type inequalities (II), http://www.staff.vu.edu.au/RGMIA/v12(E).asp.

  14. K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, Some companions of Fejer’s inequality for convex functions, http://www.staff.vu.edu.au/RGMIA/v12(E).asp.

  15. K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, On some weighted integral inequalities for convex functions related to Fejér’s result, Filomat, 24 (2010), 125–148.

    Article  MathSciNet  Google Scholar 

  16. K.-L. Tseng, G.-S. Yang and K.-C. Hsu, On some inequalities of Hadamard’s type and applications, Taiwanese J. Math., 13 (2009), 1929–1948.

    MathSciNet  MATH  Google Scholar 

  17. G.-S. Yang and M.-C. Hong, A note on Hadamard’s inequality, Tamkang J. Math., 28 (1997), 33–37.

    MathSciNet  MATH  Google Scholar 

  18. G.-S. Yang and K.-L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180–187.

    Article  MathSciNet  MATH  Google Scholar 

  19. G.-S. Yang and K.-L. Tseng, Inequalities of Hadamard’s type for Lipschitzian mappings, J. Math. Anal. Appl., 260 (2001), 230–238.

    Article  MathSciNet  MATH  Google Scholar 

  20. G.-S. Yang and K.-L. Tseng, On certain multiple integral inequalities related to Hermite-Hadamard inequalities, Util. Math., 62 (2002), 131–142.

    MathSciNet  MATH  Google Scholar 

  21. G.-S. Yang and K.-L. Tseng, Inequalities of Hermite-Hadamard-Fejér type for convex functions and Lipschitzian functions, Taiwanese J. Math., 7 (2003), 433–440.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Aletheia University, Tamsui, Taiwan, 25103

    Kuei-Lin Tseng

  2. China University of Science and Technology, Nankang, Taipei, Taiwan, 11522

    Shiow-Ru Hwang

  3. School of Engineering and Science, Victoria University, Melbourne, Victoria, Australia

    S. S. Dragomir

  4. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg, South Africa

    S. S. Dragomir

Authors
  1. Kuei-Lin Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiow-Ru Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. S. Dragomir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kuei-Lin Tseng.

Additional information

Communicated by Dénes Petz

Partially supported by grant NSC 98-2115-M-156-004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tseng, KL., Hwang, SR. & Dragomir, S.S. Refinements of Fejér’s inequality for convex functions. Period Math Hung 65, 17–28 (2012). https://doi.org/10.1007/s10998-012-3980-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-012-3980-7

Mathematics subject classification number

Key words and phrases

Search

Navigation