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1
Content available remote Remarks on the certain subclass of univalent functions
Piejko K., Trojnar-Spelina L.
Journal of Mathematics and Applications
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2008
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Vol. 30
125-130
EN
We investigate the family LP α (α ∈ (-π, π]) of functions [wzór] that are analytic in the unit disk with the property that the domain of values [wzór] is the parabolic region (Imw) ² < 2Rew - 1.We give inclusion theorems and bounds of Re �'(z) for this class.
2
Content available remote Some inequalities involving differential operators and their applications to certain multivalent functions
Dziok J., Huseyin I., Piejko K.
Journal of Mathematics and Applications
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2007
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Vol. 29
109-120
EN
The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].
3
Hadamard product of certain classes of functions
Piejko K.
Journal of Applied Analysis
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2005
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Vol. 11, nr 1
145-151
EN
In this paper we consider the Hadamard product * of regular functions using the concept of subordination. Let P(A,B) denote the class of regular functions subordinated to the linear fractional transformation (1 + Az)/(1 - Bz), where A + B ≠ 0 and \B\ ≤ 1. By P(A,B)* P(C,D) we denote the set, {f * g : f ∈ P(A,B), g ∈ P(C,D)}. It is known ([3], [7]). that for some complex numbers A,B,C,D there exist X and Y such that P(A, B) * P(C, D) ⊂ P(X, Y). The purpose of this note is to find the necessary and sufficient conditions for the equality of the classes P(A, B) * P(C, D) and P{X, Y).
4
Content available remote Convolution properties of a class of analytic functions
Piejko K., Sokół J.
Demonstratio Mathematica
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2004
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Vol. 37, nr 1
63--69
EN
In this paper we consider convolution properties of a class of bounded analytic functions investigated by J. Stankiewicz and Z. Stankiewicz in [6]. We give some examples which verify a conjecture connected with this paper.
5
Content available remote On some convolution theorems
Piejko K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2002
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[Z] 42(1)
103-112
EN
Let ℌ be the class of functions regular in the unit disc. For two functions ƒ(z) = [formula], g (z) = [formula] of the class ℌ and for all complex m we define the convolution (ƒ★m g) (z) [formula]. For given complex numbers a, A, B; aB ≠ A, |B| ≤ 1 we define Pa (A, B) := [formula]. The object of this paper is to give the solution of the problem of finding all m ϵ C, for which convolution ƒ★m g belongs to the Pab (X. Y) if ƒ ϵ Pa (A, B) and g ϵ Pb (C, D).
6
Sploty funkcji o dowolnych normalizacjach
Piejko K., Stankiewicz J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2001
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z. 25 [190]
175-183
EN
Let [delta] be the unit disc and H the class of all regular functions in A. For two functions [...].
7
Obszary dwukątowe i sploty funkcji
Piejko K.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2001
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z. 25 [190]
167-174
EN
Let [delta] be the unit disc and H the class of regular functions in A. For two functions [...].
8
Content available remote Convolution of functions with free normalization
Piejko K., Stankiewicz J.
Demonstratio Mathematica
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2001
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Vol. 34, nr 1
69-76
9
Some circular biangularly domains and convolution of functions
Piejko K.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2000
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z. 24 [181]
103-109
EN
Let [delta] denotes the unit disc and let H be the class of functions regular in [delta]. By N we denote the family of functions from H normalized by condition f(O) = 1. For two functions [...].
10
Convolution of functions mappings the unit disc into some ngularly domains
Piejko K.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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1999
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z. 23 [175]
105-110
EN
Let delta denotes the unit disc and let [...].
11
Content available remote Note on Robinson's functional equation
Piejko K.
Demonstratio Mathematica
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1999
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Vol. 32, nr 4
713-715
EN
The purpose of this note is to give a new proof of the fact, that the only entire solutions of the Robinson's functional equation are given by f(z) = Az or f(z) = A sin az, where A, a are complex constants and a is real or purely imaginary.
12
Convolution of functions which take values in some special angularly domains of complex plane
Piejko K., Stankiewicz J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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1998
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z. 22 [170]
131-138
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