A unified approach to radius of convexity problems for certain classes of univalent analytic functions.
We continue our previous work on a problem of Janiec connected with a uniqueness theorem, of Cartan-Gutzmer type, for holomorphic mappings in ℂⁿ. To solve this problem we apply properties of (j;k)-symmetrical functions.
A sufficient univalence condition for meromorphic functions is given
We give a necessary and sufficient condition for an analytic function in to have real part in class . This condition contains the classical one of Zygmund; other variants are also given.
The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy . Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.
In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane.
Let H be a group of conformal automorphisms of a closed Riemann surface S, isomorphic to either of the alternating groups A4 or A5 or the symmetric groups S4 or S5. We provide necessary and sufficient conditions for the existence of a Schottky uniformization of S for which H lifts. In particular, togheter with the previous works in Hidalgo (1994,1999), we exhaust the list of finite groups of Möbius transformations of Schottky type.