Hadamard type inequalities for φ-convex functions on the co-ordinates

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In this paper, we introduce the notation of φ-convex functions on the co-ordinates and present some properties. Also, new Hadamard type inequalities for such functions are obtained.

[1] G. Cristescu and L. Lupsa, Non-connected convexities and applications, Kluwer Academic Publishers Dordrecht / Boston / London, 2002.

[2] G. Cristescu, Hadamard type inequalities for φ-convex functions, Annals of the University of Oradea, Fascicle of Management and Technological Engineering, C-Rom Edition, III (XIII), 2004.

[3] M.K. Bakula and J. Pecaric, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.

[4] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Appications, RGMIA Monographs, Victoria University, 2000.

[5] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11(5) (1998), 91-95.

[6] S.S. Dragomir and B. Bond, Integral inequalities of Hadamard type for log-convex functions, Demonstratio Math., 31(1998), 354-364.

[7] C.E.M. Pearce, J. Pecaric, V. Simic, Stolarsky means and Hadamard's inequality, J. Math. Anal. Appl., 220 (1998), 99-109.

[8] J.E. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, 1992.

[9] E.A. Youness, E-convex Sets, E-convex Functions and E-convex Programming, Journal of Op- timization Theory and Applications, 102, 2(1999), 439-450.

[10] M.A. Latif and M. Alomari, On Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. Journal of Math. Analysis, 33, 2009, 1645-1656.

[11] M. Z. Sarikaya, On Hermite Hadamard-type inequalities for strongly '-convex functions, South- east Asian Bull. Math., in press.

[12] M. Z. Sarikaya, On Hermite Hadamard-type inequalities for 'h-convex functions, Kochi Jour- nal of Mathematics, 9 (2014), 83-90 .

[13] M. Z. Sarikaya, On strongly 'h-convex functions in inner product spaces, Arabian Journal of Mathematics, (2013) 2:295{302.