SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS

Year 2011, Volume: 40 Issue: 2, 219 - 229, 01.02.2011

M.e. Özdemir E. Set Erhan Set  m.z. Sarıkaya

https://izlik.org/JA48GS73SN

Abstract

In this paper, we establish some new Hermite-Hadamard type inequalities for m-convex and (α, m)-convex functions of 2-variables on the co-ordinates

Keywords

m-convex function , co-ordinated convex mapping , Hermite-Hadamard inequality

SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS

https://izlik.org/JA48GS73SN

Abstract

References

• Alomari, M. and Darus, M. Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sciences 3 (32), 1557–1567, 2008.
• Bakula, M. K. ¨Ozdemir, M. E. and Peˇcari´c, J. Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure and Appl. Math. 9 (4), Art. 96, 2008.
• Bakula, M. K., Peˇcari´c, J. and Ribiˇci´c, M. Companion inequalities to Jensen’s inequality for m-convex and(α, m)-convex functions, J. Inequal. Pure and Appl. Math. 7 (5), Art. 194, 2006.
• Dragomir, S. S. On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics 4, 775–788, 2001.
• Dragomir, S. S. and Pearce, C. E. M. Selected Topics on Hermite-Hadamard Inequal- itiesand Applications http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
• Victoria University, 2000). [Online:
• Dragomir, S. S. and Toader, G. Some inequalities for m-convex functions, Studia Univ. Babes- Bolyai, Mathematica 38 (1), 21–28, 1993.
• Mihe¸san, V. G. A generalization of the convexity (Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, Romania, 1993).
• Toader, G. Some generalizations of the convexity, Proc. Colloq. Approx. Opt. Cluj-Napoca, 329–338, 1984.
• Set, E., Sardari, M., Ozdemir, M. E. and Rooin, J. On generalizations of the Hadamard inequality for(α, m)-convex functions, RGMIA Res. Rep. Coll. 12 (4), Article 4, 2009.