eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-06-23 7 3 85 90 10.12691/tjant-7-3-5 TJANT2019735 article Kerim Bekar kebekar@gmail.com 1 Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Türkiye In this work, by using an integral identity together with both the Hölder integral inequality and the power-mean integral inequality we establish several new inequalities for three-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. http://pubs.sciepub.com/tjant/7/3/5/tjant-7-3-5.pdf convex function arithmetic-harmonically-convex function Hermite-Hadamard’s inequality