EUDML

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On the coefficients of starlike functions of some classes

Zbigniew Jerzy Jakubowski — 1972

Annales Polonici Mathematici

On some applications of the Clunie method

Zbigniew Jerzy Jakubowski — 1972

Annales Polonici Mathematici

On typical-real functions

Zbigniew Jerzy Jakubowski — 1983

Annales Polonici Mathematici

On an estimate of a functional in the class of holomorphic univalent functions

Zbigniew Jerzy Jakubowski; Krystyna Zyskowska — 1993

Mathematica Bohemica

Let $S$ denote the class of functions $f (x) = z + a_{2} z^{2} + a_{3} z^{3} + ...$ univalent and holomorphic in the unit disc $Δ = {z : |z| < 1}$ . In the paper we obtain an estimate of the functional $|a_{3} - c a_{2}^{2}| + c {|a_{2}|}^{n}$ in the class $S$ for arbitrarily fixed $x \in 𝐑$ and $n = 1, 2, 3, ...$ . Hence, for some special values of the parameters, we obtain estimates of several interesting functionals and numerous applications. A few open problems of a similar type are also formulated.

On some applications of harmonic measure in the geometric theory of analytic functions

Jaroslav Fuka; Zbigniew Jerzy Jakubowski — 1994

Mathematica Bohemica

On estimates of functionals in some classes of functions with positive real part

Jaroslav Fuka; Zbigniew Jerzy Jakubowski — 1996

Mathematica Slovaca

On some properties of the class $𝒫 (B, b, α)$

Jaroslav Fuka; Zbigniew Jerzy Jakubowski — 1997

Mathematica Bohemica

Applications of the Hadamard product in geometric function theory

Zbigniew Jerzy Jakubowski; Piotr Liczberski; Łucja Żywień — 1991

Mathematica Bohemica

Let $𝒜$ denote the set of functions $F$ holomorphic in the unit disc, normalized clasically: $F (0) = 0, F^{'} (0) = 1$ , whereas $A \subset 𝒜$ is an arbitrarily fixed subset. In this paper various properties of the classes $A_{α}, α \in C {- 1, - \frac{1}{2}, ...}$ , of functions of the form $f = F * k_{α}$ are studied, where $F \in . A$ , $k_{α} (z) = k (z, α) = z + \frac{1}{1 + α} z^{2} + ... + \frac{1}{1 + (n - 1) α} z^{n} + ...$ , and $F * k_{α}$ denotes the Hadamard product of the functions $F$ and $k_{α}$ . Some special cases of the set $A$ were considered by other authors (see, for example, [15],[6],[3]).