[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2014.303

ON HERMITE-HADAMARD-TYPE INEQUALITIES FOR DIFFERENTIABLE QUASI-CONVEX FUNCTIONS ON THE CO-ORDINATES

Chen, Feixiang (School of Mathematics and Statistics, Chongqing Three Gorges University)

Publication Information

Journal of applied mathematics & informatics / v.32, no.3_4, 2014 , pp. 303-314 More about this Journal

Abstract

In this paper, a new lemma is established and several new inequalities for differentiable co-ordinated quasi-convex functions in two variables which are related to the left-hand side of Hermite-Hadamard type inequality for co-ordinated quasi-convex functions in two variables are obtained.

Keywords

Hermite-Hadamard's inequality; quasi-convex functions on the co-ordinates; H $\ddot{o}$ lder's inequality; power mean inequality;

Citations & Related Records

Reference

1	M. E. Ozdemir, A. O. Akdemir and Cetin Yildiz, On co-ordinated quasi-convex functions.Czechoslovak Math. J., 62(4), 2012, 889-900. DOI
2	M. Z. Sarikaya, Erhan. Set, M. E. Ozdemir and S. S. Dragomir, New some Hadamard'stype inequalities for co-ordinated convex functions. Tamsui Oxf. J. Inf. Math. Sci., 28(2),2012, 137-152.
3	M. Alomari and M. Darus, The Hadamard's inequality for s-convex functions of 2-variables on the co-ordinates. Int. Journal of Math. Analysis., 2(13), 2008, 629-638.
4	M. Alomari and M. Darus, Hadamard-Type inequalities for s-convex functions. Int. Math. Forum., 3(40), 2008, 1965-1975.
5	M. Alomari and M. Darus, On the Hadamard's inequality for log-convex functions on the coordinates. J. Inequal. Appl., 2009, 2009: 283147. DOI ScienceOn
6	S. S. Dragomir, On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math., 5(4), 2001, 775-788. DOI
7	M. A. Latif and M. Alomari, On Hadamard-type inequalities for h-convex functions on the co-ordinates. Int. Journal of Math. Analysis., 3(33), 2009, 1645-1656.
8	M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions. J. Inequal. Appl., 2012, 2012:28. DOI
9	M. E. Ozdemir, H. Kavurmaci, A. O. Akdemir and M. Avci, Inequalities for convex and s-convex functions on ${\Delta}=[a,b]{\times}[c,d]$ . J. Inequal. Appl., 2012, 2012:20. DOI
10	M. E. Ozdemir, Cetin Yildiz and A. O. Akdemir, On some new Hadamard-type inequalitiesfor co-ordinated quasi-convex functions. Hacet. J. Math. Stat., 41(5), 2012, 697-707.