NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX

Abstract

In this paper some Hermite-Hadamard type inequalities for convex functions of three variables on a rectangular box in $\mathbb{R}^3$ are given.

Keywords

• Co-ordinated convex functions,rectangular box,Hermite-Hadamard inequality

References

1. [1] A. Barani, S. Barani, Hermite-Hadamard inequalities for functions when a power of the absolute value of the rst derivative is P-convex, Bull. Aust. Math. Soc, 86 (2012), 126-134.
2. [2] A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012, 2012:247.
3. [3] S.S. Dragomir, Two renements of Hadamard's inequalities, Coll. Pap. of the Fac. of Sci. Kragujevac (Yugoslavia) 11 (1990), 23-26. ZBL No. 729: 26017.
4. [4] S.S. Dragomir, A mapping in connection to Hadamard's inequality, An Ostro. Akad. Wiss. Math. -Natur (Wien) 128 (1991), 17-20. MR 93h: 26032. ZBL No. 747: 26015.
5. [5] S.S. Dragomir, On Hadamard's inequality for convex functions, Math. Balkanica., 6 (1992), 215-222. MR 934: 26033.
6. [6] S.S. Dragomir, A renement of Hadamard's inequality for isotonic linear functionals, Tamkang J. Math., 24 (1993), 101-106.
7. [7] S.S. Dragomir, Two mappings in connection to Hadamard's inequality, J. Math. Anal. Appl. 167 (1992), 49-56. MR 93m: 26038. ZBL No. 758: 26014.
8. [8] S.S. Dragomir, Some renements of Hadamard's inequalities, Gaz. Mat. Metod. (Romania) 11 (1990), 189-191.

9. [9] S.S. Dragomir, Some integral inequalities for differentiable convex functions, Contributions, Macedonian Acad. of sci. and arts., (Scopie) 16 (1992), 77-80.
10. [10] S.S. Dragomir, D.M. Milosevic and J. Sandor, On some renements of Hadamard's inequalities and applications, Univ. Beograd, Publ. Elektrotelm. Fak., Ser. Mat., 4 (1993), 3-10.
11. [11] S.S. Dragomir, On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plan, Taiwan J. Math., 5 (2001), 775-778.
12. [12] A.G. Ghazanfari, A. Barani, Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions, Banach J. Math. Anal., 9 (2015), 9-20.
13. [13] M.A. Latif, Some inequalities for differentiable prequasiinvex functions with applications, KJM., 1 (2013), 17-29.
14. [14] M.E. Özdemir, A.O. Akdemir, Ç.Yıldız, On the co-ordinated convex functions, Appl. Math. Info. Sci., 8 (2014), 1085-1091.
15. [15] M.E. Özdemir, A.O. Akdemir, On some Hadamard-type inequalities for convex functions on a rectanfuler box, volume 2011, year 2011 article ID jnaa-00101, 10 pages doi:10.5899/2011/jnaa-00101
16. [16] J.E. Pecaric and S.S. Dragomir, On some integral inequalities for convex functions, Bull. Mat. Inst. Pol. Iasi, 36 (1990), 19-23.
17. [17] J.E. Pecaric and S.S. Dragomir, A generalization of Hadamard's inequality for isotonic linear functionals, Rodovi Math., (Sarajevo) 7 (1991), 103-107. 26026.
18. [18] M.Z. Sarıkaya, Erhan. Set, M.E. Özdemir and S.S. Dragomir, New some Hermite-Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences., 28 (2012), 137-152.
19. [19] D.Y. Wang, K.L. Tseng, G.S. Yang, Some Hadamard's inequality for co-ordinated convex functions in a rectangle from the plane, Taiwan J. Math., 11 (2007), 63-73.
20. [20] B-Y. Xi, J. Hua , F. Qi, Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, Appl. Anal., 20 (2014), 29-39.