GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES VIA FRACTIONAL INTEGRALS FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX

Abstract

In this paper, the author establish some new estimates on HermiteHadamard type and Simpson type inequalities via Riemann Liouville fractionalintegral for functions whose second derivatives in absolute values at certainpower are quasi-convex

Keywords

• Quasi-convex function,Hermite–Hadamard type inequalities,Simpsontype inequalities,Riemann–Liouville fractional integral

References

1. M. Abramowitz, I.A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
2. M. Alomari and M. Darus, On some inequalities of Simpson-type via quasi-convex functions with applications, Tran. J. Math. Mech. 2 (2010), 15-24.
3. M. W. Alomari, M. Darus and S. S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. of Math., 41(4) (2010), 353-359.
4. A. Barani, S. Barani and S.S. Dragomir, Refinements of Hermite-Hadamard type inequality for functions whose second derivative absolute values are quasi convex, RGMIA Res. Rep. Col., 14 (2011).
5. D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex func- tions, Annals of University of Craiova Math. Comp. Sci. Ser., 34 (2007), 82-87.
6. I. Iscan, Generalization of different type integral inequalities for s-convex functions via frac- tional integrals, Applicable Analysis, accepted for publication, arXiv:1304.3897. I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are(α, m)−convex, Int. J. of Eng. and Appl. Sci., 2(3) (2013), 53–62.
7. I. Iscan, On generalization of some integral inequalities for quasi-convex functions and their applications, Int. J. of Eng. and Appl. Sci., 3(1) (2013), 37-42. M.Z. Sarikaya, integration, doi:1155/2012/428983. Analysis, 2012 (2012), Article ID 428983, 10 pages,
8. M. Z. Sarikaya, A. Saglam, H. Yildirim, New inequalities of Hermite-Hadamard type for func- tions whose second derivatives absolute values are convex and quasi-convex, arXiv:1005.0451 (2010).

9. M.Z. Sarikaya, E. Set, H. Yaldiz, and N. Basak, Hermite–Hadamard’s inequalities for frac- tional integrals and related fractional inequalities, Math. Comput. Model. (2012), Online, doi:1016/j.mcm.2011.12.048.
10. M.Z. Sarikaya and H. Yaldiz, On weighted Montogomery identities for Riemann-Liouville fractional integrals, Konuralp J. of Math., 1(1) (2013) 48-53.
11. E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comp. Math. Appl., 63(7) (2012), 1147-1154.
12. Giresun University, Science and Art Faculty, Department of Mathematics, Giresun- TURKEY E-mail address: [e-mail]