Alomari, M., Darus, M. and Dragomir, S.S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 9.
Bo-Yan Xi, Rui-Fang Bai and Feng Qi, Hermite–Hadamard type inequalities for the m− and (α, m) −geometrically convex functions, Aequat. Math., Springer Basel AG 2012, DOI 1007/s00010-011-0114-x.
C¸ . Yıldız, M. G¨urb¨uz and Ahmet Ocak Akdemir, The Hadamard Type Inequalities for M −Convex Functions, arXiv:1011.1543.
Dragomir, S.S., Agarwal, R.P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5 (2000), 533-579. E. Set, M. Sardari, M.E. ¨ Ozdemir and J. Rooin,
Hadamard inequality for (α, m)−convex functions, Kyungpook Math. J. 52(2012), 307-317. http://dx.doi.org/10.5666/KMJ.2012.52.3.307.
On generalizations of the G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
Liu, B.Z., An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
M. Emin ¨Ozdemir, Ahmet Ocak Akdemir and Merve Avcı, On Some Hadamard-Type In- equalities for Differentiable m−Convex Functions, arXiv:1112.3866.
M.E. ¨Ozdemir, M. Avcı, E. Set, On some inequalities of Hermite–Hadamard type via m−convexity, Appl. Math. Lett. 23 (9) (2010) 1065–1070.
M.E. ¨Ozdemir, M. Avcı and H. Kavurmacı, Hermite–Hadamard-type inequalities via (α, m)−convexity, Computers and Mathematics with Applications, 61 (2011), 2614–2620.
M.E. ¨Ozdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (α, m)−convex func- tions, Kyungpook Math. J. 50 (2010) 371–378.
M.K. Bakula, M. E ¨Ozdemir, J. Peˇcari´c, Hadamard type inequalities for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 9 (2008), Article 96.
M. Klariˇci´c Bakula, J. Peˇcari´c, M. Ribiˇci´c, Companion inequalities to Jensen’s inequality for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 7 (2006), Article 194.
M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex, RGMIA Res. Rep. Coll. 13 (1) (2010).
M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, Some new Hadamard’s type inequalities for co- ordinated m−convex and (α, m)−convex functions, Hacettepe J. of. Math. and Ist., 40, 219- 229, (2011).
S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang J. Math., 3 (1) 2002.
S.S. Dragomir and G.H. Toader, Some inequalities for m−convex functions, Studia Univ. Babe¸s-Bolyai, Math., 38 (1) (1993), 21-28.
Ujevi´c, N., Double integral inequalities of Simpson type and applications, J. Appl. Math. and Computing, 14 (2004), no:1-2, p. 213-223.
V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
Zhongxue, L., On sharp inequalities of Simpson type and Ostrowski type in two independent variables, Comp. and Math. with Appl., 56 (2008), 2043-2047.
Van Y¨uz¨unc¨u Yıl University, Faculty of Education, Department of Mathematics Ed- ucation, Van, Turkey E-mail address: havvaonalan@yyu.edu.tr A˘grı ˙Ibrahim C¸ ec¸en University, Faculty of Science and Letters, Department of Mathematics, 04100, A˘grı, Turkey
E-mail address: ahmetakdemir@agri.edu.tr Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address: erhanset@yahoo.com Department of Mathematics, Faculty of Science and Arts, D¨uzce University, Konu- ralp Campus, D¨uzce, Turkey E-mail address: sarikayamz@gmail.com
In this paper, we establish Simpson’s type inequalities for m− and(α, m) −geometrically convex functions using the lemmas
References
Alomari, M., Darus, M. and Dragomir, S.S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 9.
Bo-Yan Xi, Rui-Fang Bai and Feng Qi, Hermite–Hadamard type inequalities for the m− and (α, m) −geometrically convex functions, Aequat. Math., Springer Basel AG 2012, DOI 1007/s00010-011-0114-x.
C¸ . Yıldız, M. G¨urb¨uz and Ahmet Ocak Akdemir, The Hadamard Type Inequalities for M −Convex Functions, arXiv:1011.1543.
Dragomir, S.S., Agarwal, R.P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5 (2000), 533-579. E. Set, M. Sardari, M.E. ¨ Ozdemir and J. Rooin,
Hadamard inequality for (α, m)−convex functions, Kyungpook Math. J. 52(2012), 307-317. http://dx.doi.org/10.5666/KMJ.2012.52.3.307.
On generalizations of the G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
Liu, B.Z., An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
M. Emin ¨Ozdemir, Ahmet Ocak Akdemir and Merve Avcı, On Some Hadamard-Type In- equalities for Differentiable m−Convex Functions, arXiv:1112.3866.
M.E. ¨Ozdemir, M. Avcı, E. Set, On some inequalities of Hermite–Hadamard type via m−convexity, Appl. Math. Lett. 23 (9) (2010) 1065–1070.
M.E. ¨Ozdemir, M. Avcı and H. Kavurmacı, Hermite–Hadamard-type inequalities via (α, m)−convexity, Computers and Mathematics with Applications, 61 (2011), 2614–2620.
M.E. ¨Ozdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (α, m)−convex func- tions, Kyungpook Math. J. 50 (2010) 371–378.
M.K. Bakula, M. E ¨Ozdemir, J. Peˇcari´c, Hadamard type inequalities for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 9 (2008), Article 96.
M. Klariˇci´c Bakula, J. Peˇcari´c, M. Ribiˇci´c, Companion inequalities to Jensen’s inequality for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 7 (2006), Article 194.
M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex, RGMIA Res. Rep. Coll. 13 (1) (2010).
M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, Some new Hadamard’s type inequalities for co- ordinated m−convex and (α, m)−convex functions, Hacettepe J. of. Math. and Ist., 40, 219- 229, (2011).
S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang J. Math., 3 (1) 2002.
S.S. Dragomir and G.H. Toader, Some inequalities for m−convex functions, Studia Univ. Babe¸s-Bolyai, Math., 38 (1) (1993), 21-28.
Ujevi´c, N., Double integral inequalities of Simpson type and applications, J. Appl. Math. and Computing, 14 (2004), no:1-2, p. 213-223.
V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
Zhongxue, L., On sharp inequalities of Simpson type and Ostrowski type in two independent variables, Comp. and Math. with Appl., 56 (2008), 2043-2047.
Van Y¨uz¨unc¨u Yıl University, Faculty of Education, Department of Mathematics Ed- ucation, Van, Turkey E-mail address: havvaonalan@yyu.edu.tr A˘grı ˙Ibrahim C¸ ec¸en University, Faculty of Science and Letters, Department of Mathematics, 04100, A˘grı, Turkey
E-mail address: ahmetakdemir@agri.edu.tr Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address: erhanset@yahoo.com Department of Mathematics, Faculty of Science and Arts, D¨uzce University, Konu- ralp Campus, D¨uzce, Turkey E-mail address: sarikayamz@gmail.com