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

Research Article

Inequalities for Co-ordinated m-Convex Functions via Riemann-Liouville Fractional Integrals

  • Çetin Yildiz1*
  • Mevlüt Tunc2
  • Havva Kavurmaci
  1. Atatürk University
  2. Kilis University

* Corresponding author

Abstract

In this paper, we prove some new inequalities of Hadamard-type for m-convex functions on the co-ordinates via Riemann-Liouville fractional integrals.

How to Cite

Ç. Yildiz, M. Tunc, H. Kavurmaci, Inequalities for Co-ordinated m-Convex Functions via Riemann-Liouville Fractional Integrals, Int. J. Anal. Appl. 5 (2014), 45–55.

BibTeX
@article{Yildiz2014,
  author  = {Yildiz, Çetin and Tunc, Mevlüt and Kavurmaci, Havva},
  title   = {Inequalities for Co-ordinated m-Convex Functions via Riemann-Liouville Fractional Integrals},
  journal = {Int. J. Anal. Appl.},
  volume  = {5},
  year    = {2014},
  pages   = {45--55},
  doi     = {}
}

References

  • [1] M. Alomari and M. Darus, On the Hadamard's inequality for log -convex functions on the coordinates, Journal of Inequalities and Appl., 2009, article ID 283147.
  • [2] M.K. Bakula and J. Peˇcari ´c, On the Jensen's inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese Journal of Math., 5, 2006, 1271-1292.
  • [3] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9 (4) (2010) 493-497.
  • [4] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1 (1) (2010) 51-58.
  • [5] Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett. A., 1 (2) (2010) 155-160.
  • [6] Z. Dahmani, L. Tabharit, S. Taf, New generalizations of Gruss inequality using Riemann- Liouville fractional integrals, Bull. Math. Anal. Appl., 2 (3) (2010) 93-99.
  • [7] S.S. Dragomir, On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Math., 5, 2001, 775-788.
  • [8] R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • [9] S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, USA, 1993, p.2.
  • [10] M.E. Ozdemir, E. Set, M.Z. Sarikaya, Some new Hadamard's type inequalities for co- ¨ ordinated m-convex and (α, m)-convex functions, Hacettepe J. of. Math. and St., 40, 219- 229, (2011).
  • [11] M. E. Ozdemir, Havva Kavurmaci, Ahmet Ocak Akdemir and Merve Avci, Inequalities for ¨ convex and s-convex functions on ∆ =
  • [a, b]x
  • [c, d], Journal of Inequalities and Applications, 2012:20, doi:10.1186/1029-242X-2012-20.
  • [12] M. E. Ozdemir, M. Amer Latif and Ahmet Ocak Akdemir, On some Hadamard-type inequal- ¨ ities for product of two s-convex functions on the co-ordinates, Journal of Inequalities and Applications, 2012:21, doi:10.1186/1029-242X-2012-21.
  • [13] I. Podlubni, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [14] M.Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, arXiv:1005.1167v1 (Submitted for publication).
  • [15] M.Z. Sarikaya, E. Set, H. Yaldiz and N. Ba ¸sak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, In Press.
  • [16] M.Z. Sarikaya, E. Set, M. Emin Ozdemir and S.S. Dragomir, New some Hadamard's type ¨ inequalities for co-ordinated convex functions, Accepted.
  • [17] G. Toader, Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj-Napoca, (1984), 329-338.