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On Generalizations of the Hadamard Inequality for (α, m)-Convex Functions
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  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 3,  2012, pp.307-317
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.3.307
 Title & Authors
On Generalizations of the Hadamard Inequality for (α, m)-Convex Functions
Set, Erhan; Sardari, Maryam; Ozdemir, Muhamet Emin; Rooin, Jamal;
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In this paper we establish several Hadamard-type integral inequalities for (, m)-convex functions.
Hadamard inequality;convex functions;(, m)-convex function;
 Cited by
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Hermite–Hadamard type integral inequalities for differentiable m-preinvex and (α,m)-preinvex functions, Journal of the Egyptian Mathematical Society, 2015, 23, 2, 236  crossref(new windwow)
A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28(1994), 7-12.

M. K. Bakula, M. E. Ozdemir, J. Pecaric, Hadamard tpye inequalities for m-convex and (${\alpha}$,m)-convex functions, J. Inequal. Pure and Appl. Math., 9(4)(2008), Art. 96.

M. K. Bakula, J. Pecaric, M. Ribicic, Companion inequalities to Jensen's inequal- ity for m-convex and (${\alpha}$,m)-convex functions, J. Inequal. Pure and Appl. Math., 7(5)(2006), Art. 194.

S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math., 3(1)(2002).

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

S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babes-Bolyai, Mathematica, 38(1)(1993), 21-28.

U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir, J. Pecaric, Hadamard-tpye inequalities for s-convex functions, Appl. Math. and Comp., 193(2007), 26-35. crossref(new window)

V. G. Mihesan, A generalization of the convexity, Seminar on Functial Equations, Approx. and Convex, Cluj-Napoca (Romania) 1993.

D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.

C. P. Niculescu, L. E. Persson, Convex Functions and Their Applications, A Contemporary Approach, Canadian Math. Series Books in Mathematics, Springer, New York, 2006.

M. E. Ozdemir, M. Avci, E. Set, On some inequalities of Hermite{Hadamard type via m-convexity, Appl. Math. Lett., 23(9)(2010) 1065-1070. crossref(new window)

M. E. Ozdemir, H. Kavurmaci, E. Set, Ostrowski's type inequalities for (${\alpha}$,m)-convex functions, Kyungpook Math. J., 50(2010), 371-378. crossref(new window)

M. E. Ozdemir, M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via (${\alpha}$,m)-convexity, Computers and Mathematics with Applications, 61(2011), 2614- 2620. crossref(new window)

M. E. Ozdemir, E. Set and M. Z. Sarikaya, Some new Hadamard's type inequalities for co-ordinated m-convex and (${\alpha}$,m)-convex functions, Hacettepe J. of. Math. and Statistics, 40(2011), 219-229.

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

M. Z. Sarikaya, A. Saglam and H. Yildirim, On some Hadamard-type inequalities for h-convex functions, J. Math. Ineq., 2(3)(2008), 335-341.

A. Saglam, H. Yildirim and M. Z. Sarikaya, Some new inequalities of Hermite- Hadamard type, Kyungpook Math. J., 50(2010) 399-410. crossref(new window)

G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Opt. Cluj-Napoca, (1984), 329-338.

G. Toader, The hierarchy of convexity and some classic inequalities, J. Math. Ineq., 3(3)(2009), 305-313.