Skip to main content
SpringerLink
Log in

Some Hermite–Hadamard type inequalities for functions of generalized convex derivative

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional inequalities are proven for functions whose second derivative in absolute values are convex. Applications of the main results are 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. M. Bessenyei and Z. Páles, On generalized higher-order convexity and Hermite– Hadamard-type inequalities, Acta Sci. Math. (Szeged), 70 (2004), 13–24.

  2. W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter Konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math., 23 (1978), 13–20.

  3. H. Chen and U. N. Katugampola, Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274–1291.

  4. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91–95.

  5. S. S. Dragomir and S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687–696.

  6. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000); available at https://rgmia.org/papers/monographs/Master.pdf.

  7. H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100–111.

  8. R. N. Liu and R. Xu, Some fractional Hermite–Hadamard-type integral inequalities with s-(α,m)-convex functions and their applications, Adv. Difference Equ., 2021 (2021), Paper No. 168, 16 pp.

  9. D. S. Mitrinović and I. B. Laczković, Hermite and convexity, Aequationes Math., 28 (1985), 229–232.

  10. M. A. Noor, K. I. Noor and M. U. Awan, A new Hermite–Hadamard type inequality for h-convex functions, Creat. Math. Inform., 24 (2015), 191–197.

  11. B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6 (2003), Supplement, Article 1, https://rgmia.org/papers/v6e/convex1.pdf.

  12. M. Z. Sarikaya, A. Saglam and H. Yildirim, On some Hadamard–type inequalities for h-convex functions, J. Math. Inequal., 2 (2008), 335–341.

  13. S. Varošanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303–311.

Download references

Acknowledgement

The author expresses his gratitude to the referee for valuable suggestions that resulted in the present version of this paper.

Author information

Authors and Affiliations

  1. Institute of Applied Pedagogy, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, 6725, Szeged, Hungary

    P. Kórus

Authors
  1. P. Kórus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Kórus.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kórus, P. Some Hermite–Hadamard type inequalities for functions of generalized convex derivative. Acta Math. Hungar. 165, 463–473 (2021). https://doi.org/10.1007/s10474-021-01187-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-021-01187-x

Key words and phrases

Mathematics Subject Classification

Search

Navigation