Geometric interpretation and some analytical properties of first type s-convex function

There are at least two types of s-convex functions. This article will only discuss the properties related to the first type of s-convex function, consist of the geometric meaning, monotonicity, continuity, inclusion properties, and Jensen's inequality. The novelties of this research are the geometric meaning of first type s-convex function, the continuity at 0, inclusion properties of two s-convex function classes on an interval, and necessary and sufficient condition for Jensen's type equality. All the properties will be proved analitically.