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Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

Dimkov, Georgi, Dziok, Jacek (1998)

Serdica Mathematical Journal

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45We consider functions of the type, j=1 ... n, F(z) = z^p ∏ [ fj (z)/(z^p) ] ^αj where fj are p-valent functions starlike of order αj and aj are complex numbers. The problem we solve is to find conditions for the centre and the radius of the disc {z : |z − ω| < r}, contained in the unit disc {z : |z| < 1} and containing the origin,...

Generalized problem of starlikeness for products of close-to-star functions

Jacek Dziok (2013)

Annales Polonici Mathematici

We consider functions of the type F ( z ) = z ∏ j = 1 n [ f j ( z ) / z ] a j , where a j are real numbers and f j are β j -strongly close-to-starlike functions of order α j . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.

Geometric characterization for affine mappings and Teichmüller mappings

Zhiguo Chen (2003)

Studia Mathematica

We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.

Geometric characterization for homeomorphisms between disks

Shulong Li, Lixin Liu (2008)

Studia Mathematica

We give some characterizations for certain homeomorphisms between disks in the complex plane, and we prove some Schwarz type theorems for such homeomorphisms. Our results replace the main result of Chen [Studia Math. 157 (2003)] which we show to be false.

Geometric properties of Wright function

Sudhananda Maharana, Jugal K. Prajapat, Deepak Bansal (2018)

Mathematica Bohemica

In the present paper, we investigate certain geometric properties and inequalities for the Wright function and mention a few important consequences of our main results. A nonlinear differential equation involving the Wright function is also investigated.

Geometric rigidity of conformal matrices

Daniel Faraco, Xiao Zhong (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace SO ( n ) by an arbitrary compact set of conformal matrices, bounded away from 0 and invariant under SO ( n ) , and rigid motions by Möbius transformations.

Good metric spaces without good parameterizations.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized...

Growth of polynomials whose zeros are outside a circle

K. Dewan, Sunil Hans (2008)

Annales UMCS, Mathematica

If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.

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