Skip to main content
SpringerLink
Log in

Radical Convex Functions

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so-called radical convex functions and study their properties. We will see that such convex functions are bounded above by new curves, rather than straight lines. Applications including discrete and continuous Jensen inequalities, subadditivity behavior, Hermite–Hadamard and integral inequalities will be presented.

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. Azagra, D.: Global and fine approximation of convex functions. Proc. Lond. Math. Soc. 3(107), 799–824 (2013)

    Article  MathSciNet  Google Scholar 

  2. Bhatia, R.: Matrix Analysis. Springer, New York (1997)

    Book  Google Scholar 

  3. Mitrinovic, D.S., Lackovic, I.B.: Hermite and convexity. Aequat. Math. 28, 229–232 (1985)

    Article  MathSciNet  Google Scholar 

  4. Mitroi, F.: About the precision in Jensen–Steffensen inequality. Ann. Univ. Craiova 37(4), 73–84 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Niculescu, C.P., Persson, L.E.: Convex Functions and their Applications. A Contemporary Approach, CMS Books in Mathematics, vol. 23, 2nd edn. Springer, New York (2018)

    Book  Google Scholar 

  6. Sababheh, M., Furuichi, S., Moradi, H.R.: Composite convex functions. J. Math. Ineq. (in press)

  7. Sababheh, M., Moradi, H.R., Furuichi, S.: Integrals refining convex inequalities. Bull. Malays. Math. Sci. Soc. 43(3), 2817–2833 (2020)

    Article  MathSciNet  Google Scholar 

  8. Sababheh, M.: Means refinements via convexity. Mediterr. J. Math. 14, 125 (2017). https://doi.org/10.1007/s00009-017-0924-8

    Article  MathSciNet  MATH  Google Scholar 

  9. Sababheh, M.: Improved Jensen’s inequality. Math. Inequal. Appl. 17(2), 389–403 (2017)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referee for his/her valuable comments, which have considerably improved the presentation and quality of this paper.

Author information

Authors and Affiliations

  1. Department of Basic Sciences, Princess Sumaya University For Technology, Al Jubaiha, Amman, 11941, Jordan

    Mohammad Sababheh

  2. Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran

    Hamid Reza Moradi

Authors
  1. Mohammad Sababheh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid Reza Moradi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Sababheh.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sababheh, M., Moradi, H.R. Radical Convex Functions. Mediterr. J. Math. 18, 137 (2021). https://doi.org/10.1007/s00009-021-01784-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-021-01784-8

Keywords

Mathematics Subject Classification

Search

Navigation