A variational method for starlike functions

A Variational Method for Hyperbolically Convex Functions

In this paper we recall our variational method, based on Julia’s formula for the Hadamard variation, for hyperbolically convex polygons. We use this variational method to prove a general theorem for solving extremal problems for hyperbolically convex functions. Special cases of this theorem provide independent proofs for controlling growth and distortion for hyperbolically convex functions.

Horadam Polynomials Estimates for $lambda$-Pseudo-Starlike Bi-Univalent Functions

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

A New Criterion for Multivalent Starlike Functions

The main purpose of the present paper is to derive a new criterion for mul-tivalent starlike functions by applying Jack's lemma.

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