Convex Functions

A subset of \(\mathbb {C}\) is said to be convexConvex region  if the line segment joining any two of its points lies entirely within the set. An analytic function \(f:\mathbb {D}\rightarrow \mathbb {C}\) whose image \(f(\mathbb {D})\) is convex is called aFunctionconvex convex function.Convex function  The class of convex functions is studied in this chapter. An analytic characterization of convexity is established and subsequently used to derive several properties of such functions.