MϕA-h-Convexity and Hermite-Hadamard Type Inequalities

Main Article Content

Sanja Varošanec


We investigate a family of MϕA-h-convex functions, give some properties of it and several inequalities which are counterparts to the classical inequalities such as the Jensen inequality and the Schur inequality. We give the weighted Hermite-Hadamard inequalities for an MϕA-h-convex function and several estimations for the product of two functions.

Article Details


  1. M.W. Alomari, Some Properties of h − MN-Convexity and Jensen’s Type Inequalities, J. Interdiscip. Math. 22 (2019), 1349–1395. https://doi.org/10.1080/09720502.2019.1698402.
  2. I.A. Baloch, M. de la Sen, I. Iscan, Characterizations of Classes of Harmonic Convex Functions and Applications, Int. J. Anal. Appl. 17 (2019), 722–733. https://doi.org/10.28924/2291-8639-17-2019-722.
  3. M. Bombardelli, S. Varošanec, Properties of h-Convex Functions Related to the Hermite-Hadamard-Féjer Inequalities, Computers Math. Appl. 58 (2009), 1869–1877. https://doi.org/10.1016/j.camwa.2009.07.073.
  4. T.H. Dinh, K.T.B. Vo, Some Inequalities for Operator (p, h)-Convex Functions, Linear Multilinear Algebra, 66 (2018), 580–592. https://doi.org/10.1080/03081087.2017.1307914.
  5. Z.B. Fang, R. Shi, On the (p, h)-Convex Function and Some Integral Inequalities, J. Inequal. Appl. 2014 (2014), 45. https://doi.org/10.1186/1029-242X-2014-45.
  6. L.V. Hap, N.V. Vinh, On some Hadamard-Type Inequalities for (h, r )-Convex Functions, Int. J. Math. Anal. 7 (2013), 2067–2075. https://doi.org/10.12988/ijma.2013.28236.
  7. F.C. Mitroi, C.I. Spiridon, Hermite-Hadamard Type Inequalities of Convex Functions With Respect to a Pair of Quasi-Arithmetic Means, Math. Rep. 14 (2012), 291–295.
  8. C.P. Niculescu, L.E. Persson, Convex Functions and Their Applications: A Contemporary Approach, Springer New York, New York, NY, 2006. https://doi.org/10.1007/0-387-31077-0.
  9. M.A. Noor, F. Qi, M.U. Awan, Some Hermite–Hadamard Type Inequalities for Log-h-Convex Functions, Analysis. 33 (2013), 367–375. https://doi.org/10.1524/anly.2013.1223.
  10. M.A. Noor, K.I. Noor, M.U. Awan, et al. Some Integral Inequalities for Harmonically h-Convex Functions, U.P.B. Sci. Bull. Ser. A. 77 (2015), 5–16.
  11. M.Z. Sarikaya, A. Saglam, H. Yildirim, On Some Hadamard-Type Inequalities for h-Convex Functions, J. Math. Inequal. 2 (2008), 335–341.
  12. S. Turhan, M. Kunt, I. Iscan, Hermite-Hadamard Type Inequalities for MϕA-Convex Functions, Int. J. Math. Model. Comput. 10 (2020), 57–75.
  13. S. Varošanec, On h-Convexity, J. Math. Anal. Appl. 326 (2007), 303–311. https://doi.org/10.1016/j.jmaa.2006.02.086.
  14. S. Wu, M.U. Awan, M.A. Noor, et al. On a New Class of Convex Functions and Integral Inequalities, J. Inequal. Appl. 2019 (2019), 131. https://doi.org/10.1186/s13660-019-2074-y.
  15. D. Zhao, T. An, G. Ye, et al. On Hermite-Hadamard type Inequalities for Harmonical h-Convex Interval-Valued Functions, Math. Inequal. Appl. 23 (2020), 95–105. https://doi.org/10.7153/mia-2020-23-08.