The radial growth of univalent functions

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.

Univalent Functions with Univalent Derivatives. Ii

Neighbourhoods of Univalent Functions

The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also pr...

Univalent functions of fast growth with gap power series

We construct univalent functions in the unit disc, whose coefficient sequences (an) have arbitrarily long intervals of zeros, and at the same time arbitrarily long intervals where |an| > n n holds, ( n) being an an arbitrary prescribed sequence of positive numbers tending to zero. Furthermore we show that the initial interval of coefficients of such a function can be prescribed to be any interi...

Coefficients of Univalent Functions

The interplay of geometry and analysis is perhaps the most fascinating aspect of complex function theory. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior. A function is said to be univalent (or schlichi) if it never takes the same value twice: f(z{) # f(z2) if zx #= z2. The present survey will focus upon the class S ...