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On the univalent, bounded, non-vanishing and symmetric functions in the unit disk

J. Śladkowska (1996)

Annales Polonici Mathematici

The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.

On the Various Bisection Methods Derived from Vincent’s Theorem

Akritas, Alkiviadis, Strzeboński, Adam, Vigklas, Panagiotis (2008)

Serdica Journal of Computing

In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...

On the zeros of polynomials and analytic functions

Roshan Lal, Susheel Kumar, Sunil Hans (2011)

Annales UMCS, Mathematica

For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.

On two new functional equations for generalized Joukowski transformations

M. Baran, H. Haruki (1991)

Annales Polonici Mathematici

The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function 1 / 2 ( z + z - 1 ) of a complex variable z.

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