International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Some New Estimates of Hermite-Hadamard Inequalities for Harmonically Convex Functions with Applications

  • Wen Wang1*
  • Jibing Qi
  1. Hefei Normal University

* Corresponding author

Abstract

In this paper, we first establish an integral identity. Further, using this identity, some new estimates for Hermite-Hadamard inequalities for harmonically convex functions are established. Finally, some applications to special mean are showed.

How to Cite

W. Wang, J. Qi, Some New Estimates of Hermite-Hadamard Inequalities for Harmonically Convex Functions with Applications, Int. J. Anal. Appl. 13 (2017), 15–21.

BibTeX
@article{Wang2017,
  author  = {Wang, Wen and Qi, Jibing},
  title   = {Some New Estimates of Hermite-Hadamard Inequalities for Harmonically Convex Functions with Applications},
  journal = {Int. J. Anal. Appl.},
  volume  = {13},
  year    = {2017},
  pages   = {15--21},
  doi     = {}
}

References

  • [1] 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. 5 (1998), 91-95.
  • [2] J. E. Pecaric, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991.
  • [3] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, 43 (6) (2014), 935-942.
  • [4] E. Set and I. Iscan, Hermite-Hadamard type inequalities for Harmaonically convex functions on the co-ordinates, arXiv:1404.6397v1 [math.CA].
  • [5] I. Iscan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional intergrals, Applied Mathematics and Computation, 238 (2014), 237-244.
  • [6] I. Iscan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, arXiv:1310.4851v1 [math.CA].
  • [7] I. Iscan, Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions, Journal of Mathematics, 2014 (2014), Article ID 346305.
  • [8] I. Iscan, Generalization of different type integral inequalities for s-convex functions via fractional integrals, Appli- cable Analysis, 93 (9) 2014, 1846-1862.
  • [9] G. Toad er, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimiza- tion, Univ. Cluj-Napoca, Cluj-Napoca, 1985, 329-338.
  • [10] F. X. Chen and S. H. Wu, Some Hermite-Hadamard Type Inequalities for Harmonically s-Convex Functions, The Scientific World Journal, 2014 (2014), Article ID 279158.
  • [11] Tian-Yu Zhang, Feng Qi, Integral Inequalities of Hermite-Hadamard Type for m-AH Convex Functions, Turkish Journal of Analysis and Number Theory, 3(2) 2014, 60-64.
  • [12] U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (2004), 137-146.
  • [13] Kuei-Lin Tseng, Shiow-Ru Hwang, S. S. Dragomirc, New Hermite-Hadamard-type inequalities for convex functions (II), Comput. Math. Appl. 62 (2011), 401-418.
  • [14] Constantin P. Niculescu, The Hermite-Hadamard inequality for log-convex functions, Nonlinear Analysis, 75 (2012), 662-669.
  • [15] W. Wang, S. G. Yang, Schur m-power convexity of a class of multiplicatively convex functions and applications, Abstract and Applied Analysis, 2014 (2014), Article ID 258108.
  • [16] W. Wang, Ë™ I. Ë™ Iscan, H. Zhou, Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applications, Advanced Studies in Contemporary Mathematics (Kyungshang). 26 (3) (2016), 501-512.