Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 9
431
Views
24
CrossRef citations to date
0
Altmetric
Articles

Generalization of different type integral inequalities for s-convex functions via fractional integrals

Pages 1846-1862 | Received 22 Apr 2013, Accepted 27 Sep 2013, Published online: 23 Oct 2013

References

  • HudzikH, MaligrandaL. Some remarks on s-convex functions. Aequationes Math. 1994;48:100–111.
  • GorenfloR, MainardiF. Fractional calculus; integral and differential equations of fractional order. Wien: Springer Verlag; 1997. p. 223–276.
  • MillerS, RossB. An introduction to the Fractional Calculus and Fractional Differential Equations. USA: John Wiley & Sons; 1993.
  • PodlubniI. Fractional Differential Equations. San Diego: Academic Press; 1999.
  • SarikayaMZ, OgunmezH. On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012;2012:10 pages. Article ID 428983. doi:10.1155/2012/428983.
  • SarikayaMZ, SetE, YaldizH, BasakN. Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model. 2013;57:2403–2407.
  • SetE. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Comput. Math. Appl. 2012;63:1147–1154.
  • SarikayaMZ, YaldizH. On weighted Montogomery identities for Riemann-Liouville fractional integrals. Konuralp J. Math. 2013;1:48–53.
  • SarikayaMZ, SetE, OzdemirME. On new inequalities of Simpson’s type for convex functions. RGMIA Res. Rep. Coll. 2010;13:1–9. Article 2.
  • XiB-Y, QiF. Some inequalities of Hermite-Hadamard type for h-convex functions. Adv. Inequ. Appl. 2013;2:1–15.
  • AbramowitzM, StegunIA, editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover; 1965.
  • ParkJ. Hermite and Simpson-like type inequalities for functions whose second derivatives in absolute values at certain power are s-convex. Int. J. Pure Appl. Math. 2012;78:587–604.
  • IscanI. A new generalization of some integral inequalities for (α, m)-convex functions. Math. Sci. 2013;7:1–8.
  • BhattiMI, IqbalM, DragomirSS. Some new fractional integral Hermite-Hadamard type inequalities. RGMIA Res. Rep. Coll. 2013;16:1–7. Article 2.
  • ÖzdemirME, AvciM, KavurmaciH. Hermite-Hadamard-type inequalities via (α, m)-convexity. Comput. Math. Appl. 2011;61:2614–2620.
  • ParkJ. On the Simpson-like type inequalities for twice differentiable (α, m)-convex mapping. Int. J. Pure Appl. Math. 2012;78:617–634.
  • SarikayaMZ, AktanN. On the generalization of some integral inequalities and their applications. Math. Comput. Model. 2011;54:2175–2182.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.