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

Dimkov, GeorgiDziok, 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:30C45 We 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...

Classes of meromorphic multivalent functions with Montel’s normalization

Jacek Dziok — 2012

Annales UMCS, Mathematica

In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.

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.

On the extreme points of subordination families

Jacek Dziok — 2010

Annales Polonici Mathematici

We investigate extreme points of some classes of analytic functions defined by subordination and classes of functions with varying argument of coefficients. By using extreme point theory we obtain coefficient estimates and distortion theorems in these classes of functions. Some integral mean inequalities are also pointed out.

Classes of meromorphic multivalent functions with Montel’s normalization

Jacek Dziok — 2012

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.

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