Über die Koeffizienten spezieller schlichter Polynome
Über die Koeffizientensummen einiger Klassen von Potenzreihen
Über die quasikonforme Fortsetzung schlichter Funktionen.
Über Funktionen, die den Einheitskreis schlicht abbilden.
Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen
Über ungerade schlichte Funktionen.
Uniformly convex functions II
Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses . The series expansion for converges when , where depends on f. The sharp bounds on and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on and all extremal functions for n = 4, 5,...
Uniformly starlike and convex univalent functions by using certain integral operators.
Univalence for convolutions.
Univalent functions with logarithmic restrictions
It is known that univalence property of regular functions is better understood in terms of some restrictions of logarithmic type. Such restrictions are connected with natural stratifications of the studied classes of univalent functions. The stratification of the basic class S of functions regular and univalent in the unit disk by the Grunsky operator norm as well as the more general one of the class 𝔐 * of pairs of univalent functions without common values by the τ-norm (this concept is introduced...
Univalent harmonic functions.
Use of the Power inequality in connection of coefficient regions for bounded univalent functions