Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Growth and distortion theorems for a subclass of holomorphic mappings

Let X be a complex Banach space with norm ∥ · ∥, B be the unit ball in X. In this paper, we introduce a class of holomorphic mappings Mg on B. Let f(x) be a normalized locally biholomorphic mappings on B such that (Df(x))−1f(x) ∈ Mg and x = 0 is the zero of order k + 1 of f(x)− x. We investigate the growth theorem for f(x). As applications, the distortion theorems for the Jacobian matrix Jf (z)...

Two Theorems on Extensions of Holomorphic Mappings

In this paper we shall prove two theorems about extending holo-morphic mappings between complex manifolds. Both results involve extending such mappings across pseudo-concave boundaries. The first is a removable singularities statement for meromorphic mappings into compact K~ihler manifolds. The precise result and several illustrative examples are given in Section 1. The second theorem is a Hart...

Coefficient Bounds for Certain Subclasses of Bi-univalent Functions

In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions. Also, we find estimates of |a2| and |a3|. Some related consequences of the results are also pointed out. Mathematics Subject Classification: 30C45

Coefficient bounds for a new class of univalent functions involving Salagean operator and the modified Sigmoid function

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

Coefficient Estimates for Univalent Functions