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Inclusion relationships between classes of functions defined by subordination

100%
Dziok J.
Annales Polonici Mathematici
|
2011
|
tom 100
|
nr 2
193-202
EN
The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.
2
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On the extreme points of subordination families

100%
Dziok J.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 1
23-37
EN
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.
3
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Generalized problem of starlikeness for products of close-to-star functions

100%
Dziok J.
Annales Polonici Mathematici
|
2013
|
tom 107
|
nr 2
109-121
EN
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 𝓓(a,r) = {z:|z-a| < r}, |a| < r ≤ 1 - |a|, ensuring that F(𝓓(a,r)) is a domain starlike with respect to the origin.
4
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Characterizations of analytic functions associated with functions of bounded variation

100%
Dziok J.
Annales Polonici Mathematici
|
2013
|
tom 109
|
nr 2
199-207
EN
We define certain classes of functions associated with functions of bounded variation. Some characterizations of those classes are given.
5
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Classes of meromorphic multivalent functions with Montel’s normalization

100%
Dziok J.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2012
|
tom 66
|
nr 2
EN
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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