TY - JOUR T1 - ON HADAMARD TYPE INTEGRAL INEQUALITIES FOR NONCONVEX FUNCTIONS AU - Sarıkaya, Mehmet Zeki AU - , Hakanbozkurt AU - , Necmettinalp PY - 2013 DA - December JF - Mathematical Sciences and Applications E-Notes JO - Math. Sci. Appl. E-Notes PB - Murat TOSUN WT - DergiPark SN - 2147-6268 SP - 217 EP - 229 VL - 1 IS - 2 LA - en AB - In this paper, we extend some estimates of the right and left handside of a Hermite- Hadamard type inequality for nonconvex functions whosederivatives absolute values are ϕ-convex and quasi-ϕ-convex was introducedby Noor in [3] KW - Hermite-Hadamard’s inequalities KW - non-convex functions KW - H¨older’sinequality CR - S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applica- tions to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91–95. CR - S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. [3] M. Aslam Noor, Some new classes of nonconvex CR - functions, Nonl.Funct.Anal.Appl.,11(2006),165-171 CR - M. Aslam Noor, On Hadamard integral inequalities involving two log-preinvex functions, J. Inequal. Pure Appl. Math., 8(2007), No. 3, 1-6, Article 75. CR - M. Aslam Noor, Hermite-Hadamard integral inequalities for log-ϕ − convex functions, Nonl. Anal. Forum, (2009). [6] M. Aslam Noor, On a class of general variotional inequalities, J. Adv. Math. Studies, 1(2008), 31-42. CR - K. Inayat Noor and M. Aslam Noor, Relaxed strongly nonconvex functions, Appl. Math. E-Notes, 6(2006), 259-267. CR - U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146. CR - U.S. Kırmacı and M.E. ¨Ozdemir, On some inequalities for differentiable mappings and ap- plications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 153 (2004), 361-368. [10] U.S. Kırmacı, Improvement and further generalization of inequalities for differentiable map- pings and applications, Computers and Math. with Appl., 55 (2008), 485-493. CR - D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex func- tions, Annals of University of Craiova Math. Comp. Sci. Ser., 34 (2007) 82-87. CR - C.E.M. Pearce and J. Peˇcari´c, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13(2) (2000), 51–55. CR - J. Peˇcari´c, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991. CR - M. Z. Sarikaya, A. Saglam and H. Yıldırım, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex, International Journal of Open Problems in Computer Science and Mathematics ( IJOPCM), 5(3), 2012. CR - M. Z. Sarikaya, A. Saglam and H. Yıldırım, On some Hadamard-type inequalities for h-convex functions, Journal of Mathematical Inequalities, Volume 2, Number 3 (2008), 335-341. CR - M. Z. Sarikaya, M. Avci and H. Kavurmaci, On some inequalities of Hermite-Hadamard type for convex functions, ICMS Iternational Conference on Mathematical Science. AIP Confer- ence Proceedings 1309, 852 (2010). CR - M. Z. Sarikaya and N. Aktan, On the generalization some integral inequalities and their applications Mathematical and Computer Modelling, Volume 54, Issues 9-10, November 2011, Pages 2175-2182. CR - M. Z. Sarikaya, E. Set and M. E. Ozdemir, On some new inequalities of Hadamard type involving h-convex functions, Acta Mathematica Universitatis Comenianae, Vol. LXXIX, 2(2010), pp. 265-272. [19] A. Saglam, M. Z. Sarikaya and H. Yildirim, Some new inequalities of Hermite-Hadamard’s type, Kyungpook Mathematical Journal, 50(2010), 399-410. CR - C¸ . Yıldız, M. G¨urb¨uz and A. O. Akdemir, The Hadamard type inequalities for m-convex functions, Konuralp Journal of Math. Volume 1 No. 1 pp. 40–47 (2013). CR - Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce- TURKEY CR - E-mail address: sarikayamz@gmail.com, insedi@yahoo.com and placenn@gmail.com UR - https://dergipark.org.tr/en/pub/mathenot/issue//207661 L1 - https://dergipark.org.tr/en/download/article-file/182494 ER -