Sur une classe de fonctions univalentes
Taylor Series of the Natural Powers of the Pick Function and Applications
The area of the Mandelbrot set.
The Bieberbach Conjecture for Restricted Initial Coefficients.
The Bieberbach Conjecture for Univalent Functions with Small Second Coefficients.
The class of functions spirallike with respect to a boundary point.
The coefficient problem for functions with positive real part in a finitely connected domain
The Douady-Earle extension of quasihomographies
Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let denote the family of all K-quasihomographies of T. With any we associate the Douady-Earle extension and give an explicit and asymptotically sharp estimate of the norm of the complex dilatation of .
The Equivalence of Two Weak Bieberbach Conjectures.
The punishing factors for convex pairs are .
The radius of convexity of certain analytic functions. II.
The second coefficient of a function with all derivatives univalent.
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.