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

Yıl 2010, Cilt: 3 Sayı: 2, 263 - 271, 11.03.2014

Çetin Yıldız Ahmet Akdemir Merve Avcı

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

• 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.
• 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.
• 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/ ].
• 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/ ].
• 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.
• Dragomir, S.S., (1992). Two mappings in connection to Hadamard.s inequalities, J.Math. Anal. Appl., 167, 49-56.
• Dragomir, S.S. and Pearce, C.E.M., (1998). Quasi-convex functions and Hadamard's inequality, Bull. Austral. Math. Soc., 57, 377-385.
• 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.
• Kavurmacı, H., Avcı, M. and Özdemir, M.E., New Inequalities of Hermite- Hadamard Type for Convex Functions with Applications, Arxiv:1006.1593v1.
• 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.
• 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/ ].
• 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.
• 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.
• 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/ ].
• 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. ****