Title: Inequalities for Co-ordinated m−Convex Functions via Riemann-Liouville Fractional Integrals
Author(s): Çetin Yildiz, Mevlüt Tunc, Havva Kavurmaci
Pages: 45-55
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.

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.


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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. Sarıkaya, 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 Kavurmacı, Ahmet Ocak Akdemir and Merve Avcı, 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. Sarıkaya, E. Set, H. Yaldız and N. Ba¸sak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, In Press.

  18. M.Z. Sarıkaya, 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.