SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX

Öz

In this paper we establish some estimates of the right hand side of Hermite-Hadamard type inequality for functions whose derivatives absolute values are quasi-convex.

Anahtar Kelimeler

• Quasi-konveks fonksiyonlar, hölder eşitsizliği, power mean eşitsizliği

Kaynakça

1. Alomari, M., Darus, M. and Dragomir, S.S., (2009). Inequalities of Hermite- Hadamard's type for functions whose derivatives absolute values are quasi- convex, RGMIA Res. Rep. Coll., 12, Supplement, Article 14.
2. Alomari, M., Darus, M. and Dragomir, S.S., (2009). New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, RGMIA Res. Rep. Coll., 12, Supplement, Article 17.
3. Alomari, M. and Darus, M., (2010). On some inequalities Simpson-type via quasi-convex functions with applications, RGMIA Res. Rep. Coll., 13, 1, Article 8. [ http://www.staff.vu.edu.au/RGMIA/ ].
4. Alomari, M. and Darus, M., (2010). Some Ostrowski type inequalities for quasi- convex functions with applications to special means, RGMIA Res. Rep. Coll., 13, 2, Article 3. [http://www.staff.vu.edu.au/RGMIA/ ].
5. Alomari, M., Darus, M. and Kirmacı, U.S., (2010). Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means. Computers and Mathematics with Applications, 59, 225-232.
6. Dragomir, S.S., (1992). Two mappings in connection to Hadamard.s inequalities, J.Math. Anal. Appl., 167, 49-56.
7. Dragomir, S.S. and Pearce, C.E.M., (1998). Quasi-convex functions and Hadamard's inequality, Bull. Austral. Math. Soc., 57, 377-385.
8. Ion, D.A., (2007). Some estimates on the Hermite-Hadamard inequalities through quasi-convex functions, Annals of University of Craiova, Math. Comp. Sci. Ser., 34, 82-87.

9. Kavurmacı, H., Avcı, M. and Özdemir, M.E., New Inequalities of Hermite- Hadamard Type for Convex Functions with Applications, Arxiv:1006.1593v1.
10. Kirmaci, U.S., (2004). Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comp. 147, 137-146.
11. Set, E., Özdemir, M.E. and Sarıkaya, M.Z., (2010). On new inequalities of Simpson's type for quasi-convex functions with applications, RGMIA Res. Rep. Coll., 13, 1, Article 6. [http://www.staff.vu.edu.au/RGMIA/ ].
12. Sarıkaya, M.Z., Sağlam A. and Yıldırım, H., (2010). New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex, Arxiv:1005.0451v1.
13. Tseng, K.L., Hwang, S.R. and Dragomir, S.S., (2010). New Hermite-Hadamard Type Inequalities For Convex Functions, RGMIA Res. Rep. Coll., 13, 2, Article 5.
14. Tseng, K.L., Yang G.S. and Dragomir, S.S., (2003). On quasi convex functions and Hadamard's inequality, RGMIA Res. Rep. Coll., 6, 3, Article 1. [http://www.staff.vu.edu.au/RGMIA/ ].
15. Yang, G.S., Hwang, D.Y. and Tseng, K.L., (2004). Some inequalities for differentiable convex and concave mappings, Comp. Math. Appl., 47, 207-216. ****