Samaneh G. Hamidi

Coefficient Estimates for Certain Classes of Bi-Univalent Functions

A function analytic in the open unit disk is said to be bi-univalent in if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.

Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions

We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent.

Advances on the coefficient bounds for m-fold symmetric bi-close-to-convex functions

Abstract In 1955, Waadeland considered the class of m-fold symmetric starlike functions of the form and obtained the sharp coefficient bounds . Pommerenke in 1962, proved the same coefficient bounds for m-fold symmetric close-to-convex functions. Nine years later, Keogh and Miller confirmed the same bounds for the class of m-fold symmetric Bazilevic functions. Here we will show that these bounds can be improved even further for the m-fold symmetric bi-close-to- convex functions. Moreover, our results improve those corresponding coefficient bounds given by Srivastava et al that appeared in 7(2) (2014) issue of this journal. A function is said to be bi-close-to-convex in a simply connected domain if both the function and its inverse map are close-to-convex there.

Faber Polynomial Coefficients of Classes of Meromorphic Bistarlike Functions

Applying the Faber polynomial coefficient expansions to certain classes of meromorphic bistarlike functions, we demonstrate the unpredictability of their early coefficients and also obtain general coefficient estimates for such functions subject to a given gap series condition. Our results improve some of the coefficient bounds published earlier.

Coefficients of Meromorphic Bi-Bazilevic Functions

A function is said to be bi-Bazilevic in a given domain if both the function and its inverse map are Bazilevic there. Applying the Faber polynomial expansions to the meromorphic Bazilevic functions, we obtain the general coefficient bounds for bi-Bazilevic functions. We also demonstrate the unpredictability of the behavior of early coefficients of bi-Bazilevic functions.

Unpredictability of the coefficients of m-fold symmetric bi-starlike functions

In 1984, Libera and Zlotkiewicz proved that the inverse of the square-root transform of the Koebe function is the extremal function for the inverses of odd univalent functions. The purpose of this paper is to point out that this is not the case for the m-fold symmetric bi-starlike functions by demonstrating the unpredictability of the coefficients of such functions.

Starlikeness and subordination properties of a linear operator

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator L �. For functions in this class H � k (p,�;h) we estimate the coefficients. Furthermore, some subordination properties related to the operator Lare also derived.