On Generalizations of the Hadamard Inequality for (α, m)-Convex Functions |
Set, Erhan
(Department of Mathematics, Faculty of Science and Arts, Duzce University)
Sardari, Maryam (Institute for Advanced Studies in Basic Sciences) Ozdemir, Muhamet Emin (Ataturk University, K. K. Education Faculty, Department of Mathematics) Rooin, Jamal (Institute for Advanced Studies in Basic Sciences) |
1 | 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. |
2 | A. Saglam, H. Yildirim and M. Z. Sarikaya, Some new inequalities of Hermite- Hadamard type, Kyungpook Math. J., 50(2010) 399-410. DOI ScienceOn |
3 | G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Opt. Cluj-Napoca, (1984), 329-338. |
4 | G. Toader, The hierarchy of convexity and some classic inequalities, J. Math. Ineq., 3(3)(2009), 305-313. |
5 | S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. [online: http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html]. |
6 | S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babes-Bolyai, Mathematica, 38(1)(1993), 21-28. |
7 | 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. DOI ScienceOn |
8 | V. G. Mihesan, A generalization of the convexity, Seminar on Functial Equations, Approx. and Convex, Cluj-Napoca (Romania) 1993. |
9 | D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993. |
10 | C. P. Niculescu, L. E. Persson, Convex Functions and Their Applications, A Contemporary Approach, Canadian Math. Series Books in Mathematics, Springer, New York, 2006. |
11 | 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. DOI ScienceOn |
12 | M. E. Ozdemir, H. Kavurmaci, E. Set, Ostrowski's type inequalities for (,m)-convex functions, Kyungpook Math. J., 50(2010), 371-378. 과학기술학회마을 DOI ScienceOn |
13 | M. E. Ozdemir, M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via (,m)-convexity, Computers and Mathematics with Applications, 61(2011), 2614- 2620. DOI ScienceOn |
14 | M. E. Ozdemir, E. Set and M. Z. Sarikaya, Some new Hadamard's type inequalities for co-ordinated m-convex and (,m)-convex functions, Hacettepe J. of. Math. and Statistics, 40(2011), 219-229. |
15 | J. E. Pecaric, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, 1992. |
16 | A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28(1994), 7-12. |
17 | M. K. Bakula, M. E. Ozdemir, J. Pecaric, Hadamard tpye inequalities for m-convex and (,m)-convex functions, J. Inequal. Pure and Appl. Math., 9(4)(2008), Art. 96. |
18 | M. K. Bakula, J. Pecaric, M. Ribicic, Companion inequalities to Jensen's inequal- ity for m-convex and (,m)-convex functions, J. Inequal. Pure and Appl. Math., 7(5)(2006), Art. 194. |
19 | S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math., 3(1)(2002). |