A cardioid domain and starlike functions

Convex and Starlike Univalent Functions

On Uniformly Starlike Functions

These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...

On Janowski Starlike Functions

On a subclass of n-starlike functions

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f (w) = f ′(w)− 1 = 0 and w a fixed point in U . In 2005, the authors introduced the classes of functions close to convex and α-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that ...

Classes of uniformly starlike and convex functions

Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated. 1. Introduction. Let A denote the class of functions of the form f (z) = z+ ∞ n=2 a n z