applications of subordination theory to starlike functions

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

Applications of convolution and‎ ‎subordination to certain $p$-valent functions

In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.

Subordination Results and Integral Means for K−uniforly Starlike Functions

In this paper, we introduce a generalized class of k−uniformly starlike functions and obtain the subordination results and integral means inequalities . Some interesting consequences of our results are also pointed out. 2000 Mathematics Subject Classification: 30C45, 30C80.

On sufficient condition to be in a certain subclass of starlike functions defined by subordination

An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class S 1⁄21þAz 1þBz and its subclasses, where 1 6 B < A 6 1. This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. ...

Subordination by convex 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...