International Journal of Mathematical Analysis Vol. 9, 2015, no. 15, 735 - 742 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.412389 New Properties of m-Convex Functions 1 Teodoro Lara, Edgar Rosales Departamento de F´ ısica y Matem´aticas Universidad de los Andes, N. U. Rafael Rangel, Trujillo, Venezuela Jos´ e L. S´ anchez Universidad Central de Venezuela Escuela de Matem´ aticas. Caracas. Venezuela Copyright c  2014 Teodoro Lara, Edgar Rosales and Jos´ e L. S´ anchez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this research we present some properties for m- convex functions, algebraic, in- equalities of Fej´ er type, a sandwich like theorem and a result on Hyers-Ulam stability. Mathematics Subject Classification: 26A51, 39B62 Keywords: m-convex function, strongly convex function, Fej´ er type in- equalities 1. Introduction The concept of m-convex function was introduced in ([4, 7]) and since then many properties, especially inequalities, have been obtained for them. In this paper we establish and prove some additional properties of different type, namely algebraic properties, inequalities and a sandwich type theorem. 1 This research has been partially supported by Central Bank of Venezuela.