ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES

Yıl 2015, Cilt: 3 Sayı: 2, 77 - 88, 01.10.2015

B. Meftah K. Boukerrıoua

Öz

The aim of this paper is to establish some new Cebysev type inequalities involving functions whose mixed partial derivatives are (h1; h2)- convex on the co-ordinates.

Anahtar Kelimeler

Cebysev type inequalities, co-ordinates (h1; h2)-convex, integral inequality

Kaynakça

• [1] Ahmad, F., Barnett, N. S., & Dragomir, S. S. (2009). New weighted Ostrowski and Cebysev type inequalities. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e1408-e1412.
• [2] Alomari, M., & Darus, M. (2008). The Hadamard's inequality for s-convex function of 2- variables on the co-ordinates. International Journal of Math. Analysis, 2(13), 629-638.
• [3] Boukerrioua, K., Guezane-Lakoud, A.(2007). On generalization of Cebysev type inequalities. J. Inequal. Pure Appl. Math. 8,2, Art 55.
• [4] Chebyshev, P. L. (1882). Sur les expressions approximatives des integrales denies par les autres prises entre les m^emes limites. InProc.Math.Soc.Charkov(Vol.2,pp.93-98):
• [5] Dragomir, S. S. (2001). On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J Math. 4, 775{788.
• [6] Guazene-Lakoud, A. and Aissaoui, F.2011. New Cebysev type inequalities for double integrals, J. Math. Inequal, 5(4) , 453{462.
• [7] Latif, M. A., & Alomari, M. (2009). On Hadamard-type inequalities for h-convex functions on the co-ordinates. International Journal of Math. Analysis, 3(33), 1645-1656.
• [8] Pachpatte, B. G., & Talkies, N. A. (2006). On Cebysev type inequalities involving functions whose derivatives belong to Lp spaces. J. Inequal. Pure and Appl. Math, 7(2), Art 58.
• [9] Pachaptte, B. G. (2003). On some inequalities for convex functions,RGMIA Res.Rep.Coll, 6.
• [10] Pachpatte, B. G. (2006). On Cebysev-Gruss type inequalities via Pecaric's extension of the Montgomery identity. JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only], 7(1), Art 11 .
• [11] Sarikaya, M.Z., Budak, H., Yaldiz, H. (2014). Some New Ostrowski Type Inequalities for Co-Ordinated Convex Functions." Turkish Journal of Analysis and Number Theory, vol. 2, no. 5 (2014).
• [12] Sarikaya, M.Z., Budak, H., Yaldiz, H. Cebysev type inequalities for co-ordinated convex functions. Pure and Applied Mathematics Letters 2(2014)44-48.