Abstract

A new class of (h,g;m)-convex functions is presented, together with its properties, thus generalizing several varieties of convexity such as (h-m)-convex functions, (s,m)-Godunova-Levin functions or exponentially (s,m)-convex functions. Also, the Hermite-Hadamard inequality for an (h,g;m)-convex function is proved and some special results are pointed out.

Author information

Contact details are reproduced from the original publication and may be historical.

Maja Andrić

Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

maja.andric@gradst.hr

Keywords

  • Convex function
  • Hermite-Hadamard inequality

Mathematics Subject Classification

26A51, 26D15

References

  1. M. U. Awan, M. A. Noor, K. I. Noor: Hermite-Hadamard inequalities for exponentially convex functions, Appl. Math. Inf. Sci. 2/2 (2018) 405–409.https://doi.org/10.18576/amis/120215Google Scholar
  2. W. W. Breckner: Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. 23 (1978) 13–20.Google Scholar
  3. S. S. Dragomir: On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math. 33/1 (2002) 45–56.https://doi.org/10.5556/j.tkjm.33.2002.304Google Scholar
  4. S. S. Dragomir, J. Pečarić, L. E. Persson: Some inequalities of Hadamard type, Soochow J. Math. 21 (1995) 335–341.Google Scholar
  5. E. K. Godunova, V. I. Levin: Neravenstva dlja funkcii širokogo klassa, soderžaščego vypuklye, monotonnye i nekotorye drugie vidy funkcii, Vyčislitel. Mat. i. Mat. Fiz. Mežvuzov. Sb. Nauč. Trudov, MGPI, Moskva (1985) 138–142.Google Scholar
  6. N. Mehreen, M. Anwar: Hermite–Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications, J. Inequalities Appl. (2019), art. no. 92.https://doi.org/10.1186/s13660-019-2047-1Google Scholar
  7. M. A. Noor, K. I. Noor, M. U. Awan: Fractional Ostrowski inequalities for (s, m)-Godunova-Levin functions, Facta Univ. Ser. Math. Inform. 30 (2015) 489–499.Google Scholar
  8. M. E. Özdemir, A. O. Akdemir, E. Set: On (h−m)-convexity and Hadamard-type inequalities, Transylv. J. Math. Mech. 8/1 (2016) 51–58.Google Scholar
  9. X. Qiang, G. Farid, J. Pečarić, S. B. Akbar: Generalized fractional integral inequalities for exponentially (s, m)-convex functions, J. Inequalities Appl. (2020), art. no. 70.https://doi.org/10.1186/s13660-020-02335-7Google Scholar
  10. G. H. Toader: Some generalizations of the convexity, Proc. Colloq. Approx. Optim. Cluj-Napoca (1984) 329–338.Google Scholar
  11. S. Varošanec: On h-convexity, J. Math. Analysis Appl. 326 (2007) 303–311.https://doi.org/10.1016/j.jmaa.2006.02.086Google Scholar

Suggested citation

M. Andrić, J. Pečarić. “On (h,g;m)-Convexity and the Hermite-Hadamard Inequality.” Journal of Convex Analysis 29 (2022), No. 1, 257–268. https://doi.org/10.68381/jca29016

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.