Schlicht regions for entire and meromorphic functions

Schlicht regions for entire and meromorphic functions

Let f : C → C be a meromorphic function. We study the size of the maximal disc in C with respect to spherical metric, in which a singlevalued branch of f−1 exists. The problem is related to normality and type criteria. Best possible lower estimates of the size of such discs are obtained for entire functions and a class of meromorphic functions containing all elliptic functions. An estimate for ...

Uniqueness theorems of entire and meromorphic functions sharing small function

In this paper, we deal with some uniqueness theorems of two transcendental meromorphic functions with their non-linear differential polynomials sharing a small function. These results in this paper improve those given by of Fang and Hong [M.L.Fang and W.Hong,A unicity theorem for entire functions concerning differential polynomials,Indian J.Pure Appl.Math.32.(2001),No.9,1343-1348.], I.Lahiri an...

The Schwarzian Derivative and Schlicht Functions

It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...

A Coefficient Inequality for Schlicht Functions

The Coefficients of Schlicht and Allied Functions

regular and schlicht (univalent) in | z | < 1, i.e. assuming distinct values w for distinct values of z. The functions f(z) e S map | z | < 1 1 : 1 conformally onto a simply connected domain D in the w plane. During the last international Congress at Harvard Professors Schaeffer and Spencer [12] reported on the progress, largely due to their own work, on the so-called coefficient problem for S,...