Regions of variability for a class of analytic and locally univalent functions defined by subordination

Certain Inequalities for a General Class of Analytic and Bi-univalent Functions

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

Subordination Results for a Class of Analytic Functions Defined by a Linear Operator

In this paper, we derive several interesting subordination results for certain class of analytic functions defined by the linear operator L(a, c)f(z) which introduced and studied by Carlson and Shaffer [2].

Certain Subordination Results For A Class Of Analytic Functions Defined By The Generalized Integral Operator

We obtain several interesting subordination results for a class of analytic functions defined by using a generalized integral operator. Keywords—Analytic functions, Hadamard product, Subordinating factor sequence

Regions of Variability for Univalent Functions

Let S be the standard class of univalent functions in the unit disk, and let So be the class of nonvanishing univalent functions g with g(0) = 1. It is shown that the regions of variability {g(r): g £ So} and {(1 — r2)f'(r) : f £ S} are very closely related but are not quite identical. Let 5 be the class of functions / analytic and univalent in the unit disk D, with /(0) = 0 and /'(O) = 1. Let ...

On Certain Subclasses of Analytic Functions Defined by Differential Subordination