%0 Journal Article %T (m,r)-Convex Functions %A Huriye Kadakal %J Turkish Journal of Analysis and Number Theory %D 2019 %R 10.12691/tjant-7-1-5 %X 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 %U http://www.sciepub.com/TJANT/abstract/10420