The concept of convexity and its various generalizations is important for quantitative and qualitative studies in operations research or applied mathematics. Recently, E-convex sets and E-convex functions were introduced by Youness [2], and they have some important applications in various branches of mathematical sciences. Youness in [2] introduced a class of sets and functions which is called E-convex sets and E-convex functions by relaxing the definition of convex sets and convex functions. Xiusu Chen [1] introduced a new concept of semi E-convex functions and discussed its properties. According to Xiusu Chen [1], if a function f from M to R is semi-E-convex on an E-convex set M ⊂ Rn then, f (E(x)) ≤ f (x) for each x in M. In this article we have discussed
the inverse of this proposition and present some results for convex functions.