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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 value distribution of differential polynomials of meromorphic functions

Yan Xu, Huiling Qiu (2010)

Annales Polonici Mathematici

Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and φ = R e P , where R ≢ 0 is a rational function and P is a polynomial, and let a , a , . . . , a k - 1 be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and f = 0 f ( k ) + a k - 1 f ( k - 1 ) + + a f = 0 , then f ( k ) + a k - 1 f ( k - 1 ) + + a f - φ has infinitely many zeros.

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 weighted estimate of the Bergman projection

Benoît Florent Sehba (2018)

Czechoslovak Mathematical Journal

We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.

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