Mapping Radius of Regular Function and Center of Convex Region
Wenxi Duan · Advances in computer science research · 2015
There is only a univalent and regular function in a simply connected region.It transforms the region into a unit circle, while satisfies that the function value of a point is equal to zero and the derivative of this point is greater than zero, then the inverse of the derivative is named as the mapping radius of the function at the point.The mapping radius is changing according to the movement of the point.In fact, the mapping radius in the region is a real valued function.The function is continuous and reaches the maximum value within the region.If a simply connected region is the convex region with the symmetrical center, then the mapping radius function of the region obtains the maximum at the symmetrical center of the region.