Science and Education Publishing Turkish Journal of Analysis and Number Theory 2 2 2014 04 21 Some Results on Hermite-Hadamard Type Inequality through Convexity 53 59 EN Shahid Qaisar Sabir Hussain College of Mathematics and Statistics, Chongqing University, Chongqing, P. R. China TJANT2014225 10.12691/tjant-2-2-5 2014 03 23 2014 04 20 2014 04 21 Our aim in this article to establish various inequalities for some differentiable mapping that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are convex. The new integral inequalities are then applied to some special means and as well as numerical integration to obtain some better estimates.