Variations for bounded nonvanishing univalent functions

Nonvanishing Univalent Functions*

The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + . . , analytic, univalent, and nonvanishing ...

On Nonvanishing Univalent Functions with Real Coefficients*

S O u {1} is a compact subset of A. Duren and Schober had been interested in extreme points and support points of S o. Recall that a support point of a family F is a function which maximizes the real part of some continuous linear functional, that is not constant over F. We shall give a characterization of the extreme points and support points of the subfamily So(R ) of nonvanishing univalent f...

Bounded Nonvanishing Functions and Bateman Functions

We consider the family B̃ of bounded nonvanishing analytic functions f(z) = a0 + a1 z + a2 z 2 + · · · in the unit disk. The coefficient problem had been extensively investigated (see e. g. [2], [13], [14], [16], [17], [18], [20]), and it is known that |an| ≤ 2 e for n = 1, 2, 3, and 4. That this inequality may hold for n ∈ IN, is known as the Krzyż conjecture. It turns out that for f ∈ B̃ with a...

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Estimates for Univalent Functions