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

Article Sidebar

PDF
Cite as:
Çetin Yildiz, Mevlüt Tunc, Havva Kavurmaci, Inequalities for Co-ordinated m-Convex Functions via Riemann-Liouville Fractional Integrals, Int. J. Anal. Appl., 5 (1) (2014), 45-55.

Main Article Content

Çetin Yildiz, Mevlüt Tunc, Havva Kavurmaci

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.

Article Details

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 ∆ =
  12. [a, b]x
  13. [c, d], Journal of Inequalities and Applications, 2012:20, doi:10.1186/1029-242X-2012-20.
  14. 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.
  15. I. Podlubni, Fractional Differential Equations, Academic Press, San Diego, 1999.
  16. M.Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, arXiv:1005.1167v1 (Submitted for publication).
  17. 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.
  18. M.Z. Sarikaya, E. Set, M. Emin Ozdemir and S.S. Dragomir, New some Hadamard's type ¨ inequalities for co-ordinated convex functions, Accepted.
  19. G. Toader, Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj-Napoca, (1984), 329-338.