Displaying 21 – 40 of 165

Showing per page

An application of fine potential theory to prove a Phragmen Lindelöf theorem

Terry J. Lyons (1984)

Annales de l'institut Fourier

We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset U of the complex plane: if f is analytic on U , bounded near the boundary of U , and the growth of j is at most polynomial then either f is bounded or U { | z | > r } for some positive r and f has a simple pole.

Analytic formulas for the hyperbolic distance between two contractions

Ion Suciu (1997)

Annales Polonici Mathematici

In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values...

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 𝒜 is an arbitrarily fixed subset. In this paper various properties of the classes A α , α C { - 1 , - 1 2 , ... } , of functions of the form f = F * k α are studied, where F . A , k α ( z ) = k ( z , α ) = z + 1 1 + α z 2 + ... + 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]).

Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions

Sumit Nagpal, V. Ravichandran (2012)

Annales Polonici Mathematici

By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions becomes evident in the results obtained.

Boundary subordination

Adam Lecko (2012)

Annales Polonici Mathematici

We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.

Currently displaying 21 – 40 of 165