CONVEX FUNCTIONS WITH REAL DOMAIN.

A convex set in a vector space is a set of points such that whenever x sub 1, x sub 2 belong to the set, then all points of the form lambda x sub 1 1-lambdax sub 2, where lambda is in the interval 0, 1, also belong to the set. The discussion that follows deals with a certain type of function which has a convex domain. In particular, convex functions are considered whose domains are closed, bounded intervals of real numbers. In addition to defining a convex function, properties of convexity and conditions for convexity are established. These properties and conditions are then used to establish necessary and sufficient conditions for convexity.