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4 Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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Remarks on geometrical properties of Hadmard product of regular functions

Piejko Krzysztof

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

43-48

Let [...] be the class of functions regular in the unit disc. For two functions f(z) = [..].

Hadamard product of functions subordinated to homography

Piejko Krzysztof, Sokół Janusz, Stankiewicz Jan

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

49-59

We consider convolution properties of regular functions using the concept of subordination. Let P(X, Y) denote the class of regular functions subordinated to the homography 1+Xz/1-Yz. It is known [10] that for some complex numbers A,B,C,D if is an element of P(A,B) and g is an element of P(C,D), then there exist X and Y such that f *p is an element of P(X,Y). In this paper we verify the reverse question: if for each h is an element of P(X, Y) it is possible to find suitable f is an element of P(A, B) and g is an element of P(C7, D) such that h=f*g.

Remarks on some convolutions of functions

Piejko Krzysztof

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

117-126

Let[...] be the class of functions regular in the unit disc. For two functions f{z) = [...] and for all complex numbers m we define the convolution [...]. In this paper some special n=i properties of convolutions f*mg are considered. The geometric interpretation of this results are also given.

Hadamard product of Schwarz functions of analytic functions

Piejko Krzysztof, Sokół Janusz

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

127-133

In this paper we consider the class omega*omega = {f * g : f, g is an element of omega}, where omega denote the familly of Schwarz functions. We try to estimate the coeffictions of functions belonging to omega * omega.