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
Vector fields on the space of functions univalent inside the unit disk via Faber polynomials.
Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions
Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie’s conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö relation...
Zur Pseudokonvexität bei Koeffizientenkörpern schlichter Funktionen.
Доказательство Л. де Бранжа гипотезы И.М. Милина и гипотезы Л. Бибербаха.
Дополнение к статье "об одном критерии однолистности регулярных функций"
Итерационный метод уточнения необходимых условий однолистности полиномов
К вопросу об оценке коэффициентов однолистных функций
К оценкам начальных коэффициентов в классах однолистных функций
К теореме регулярности Хеймана
Коэффициентные неравенства для конформных отображений с гомеоморфным продолжением.
Критерий однолистности регулярных функций с положительной константой Хеймана