Missouri Journal of Mathematical Sciences

Hermite-Hadamard Type Inequalities for the Product of $(\alpha, m)$-Convex Function

Hong-Ping Yin and Feng Qi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In the paper, the authors establish some Hermite-Hadamard type inequalities for the product of two $(\alpha, m)$-convex functions.

Article information

Source
Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 71-79.

Dates
First available in Project Euclid: 3 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1449161369

Digital Object Identifier
doi:10.35834/mjms/1449161369

Mathematical Reviews number (MathSciNet)
MR3431117

Zentralblatt MATH identifier
1339.26072

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 41A55: Approximate quadratures

Keywords
Hermite-Hadamard type inequality $(\alpha, m)$-convex function product Hölder's integral inequality

Citation

Yin, Hong-Ping; Qi, Feng. Hermite-Hadamard Type Inequalities for the Product of $(\alpha, m)$-Convex Function. Missouri J. Math. Sci. 27 (2015), no. 1, 71--79. doi:10.35834/mjms/1449161369. https://projecteuclid.org/euclid.mjms/1449161369


Export citation

References

  • R.-F. Bai, F. Qi, and B.-Y. Xi, Hermite-Hadamard type inequalities for the $m$- and $(\alpha,m)$-logarithmically convex functions, Filomat, 27.1 (2013), 1–7; http://dx.doi.org/10.2298/FIL1301001B.
  • M. K. Bakula, M. E. Özdemir, and J. Pečarić, Hadamard type inequalities for $m$-convex and $(\alpha,m)$-convex functions, J. Inequal. Pure Appl. Math. 9.4 (2008), Article 96, 12 pages; http://www.emis.de/journals/JIPAM/article1032.html.
  • S. S. Dragomir and G. Toader, Some inequalities for $m$-convex functions, Studia Univ. Babeş-Bolyai Math., 38.1 (1993), 21–28.
  • V. G. Miheşan, A generalization of the convexity, Seminar on Functional Equations, Approx. Convex, Cluj-Napoca, 1993. (Romania)
  • B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll. 6 (2003), Article 1; http://rgmia.org/v6(E).php.
  • Y. Shuang, H.-P. Yin, and F. Qi, Hermite-Hadamard type integral inequalities for geometric-arithmetically $s$-convex functions, Analysis (Munich) 33.2 (2013), 197–208; http://dx.doi.org/10.1524/anly.2013.1192.
  • G. Toader, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj, 1985, 329–338.
  • B.-Y. Xi and F. Qi, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl., 18.2 (2013), 163–176.
  • B.-Y. Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42.3 (2013), 243–257.
  • B.-Y. Xi and F. Qi, Some inequalities of Hermite-Hadamard type for $h$-convex functions, Adv. Inequal. Appl., 2.1 (2013), 1–15.
  • B.-Y. Xi, Y. Wang, and F. Qi, Some integral inequalities of Hermite-Hadamard type for extended $(s,m)$-convex functions, Transylv. J. Math. Mechanics, 5.1 (2013), 69–84.
  • T.-Y. Zhang, A.-P. Ji, and F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Matematiche (Catania), 68.1 (2013), 229–239; http://dx.doi.org/10.4418/2013.68.1.17.