On starlike functions associated with cardioid domain

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

Neighborhoods of Starlike and Convex Functions Associated with Parabola

Let f be a normalized analytic function defined on the unit disk and fλ z : 1 − λ z λf z for 0 < λ ≤ 1. For α > 0, a function f ∈ SP α, λ if zf ′ z /fλ z lies in the parabolic region Ω : {w : |w − α| < Rew α}. Let CP α, λ be the corresponding class consisting of functions f such that zf ′ z ′/f ′ λ z lies in the region Ω. For an appropriate δ > 0, the δ-neighbourhood of a function f ∈ CP α, λ i...

Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

On Some Classes of Multivalent Starlike Functions

Classes of multivalent functions analogous to certain classes of univalent starlike functions are defined and studied. Estimates on coefficients and distortion are made, using a variety of techniques. 1. Let St denote the class of all functions/(z) = z + . . . analytic, univalent and starlike in the unit disc U. Such functions satisfy the condition Re(z/'(z)//(z)) >0,zGU. The problem of definin...