eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-02-25 7 1 23 32 10.12691/tjant-7-1-5 TJANT2019715 article Huriye Kadakal huriyekadakal@hotmail.com 1 Ministry of Education, Bulancak Bahçelievler Anatolian High School, Giresun, Turkey In this paper, we introduce a new class of extended (m,r)-convex function and we establish the Hermite-Hadamard inequality for (m,r)-convex functions. Some special cases are discussed. Results represent significant refinement and improvement of the previous results. The definition of (m,r)-convex function is given for the first time in the literature and moreover, the results obtained in special cases coincide with the well-known results in the literature. http://pubs.sciepub.com/tjant/7/1/5/tjant-7-1-5.pdf convex function r-convex function m-convex function (m,r)-convex Hermite-Hadamard inequality