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Some application of theGolusinvariation to the starlike functions with respect to m-symmetric points

Stankiewicz Jan, Szpila Anna

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

61-68

In this paper we consider the class of starlike functions with respect to m-symmetric points. Using the integral formula for functions from this class and applying the Golusin variation of the first type we obtain a sharp lower bound for If'(z)I.

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.

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On some subclasses of starlike meromorphic functions with fixed points

Stankiewicz Jan, Szpila Anna

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

141-154

In this paper we study meromorphic k-valent functions in the unit disc with k different poles at fixed points. We investigate the class M*/k (p,wo) consisting of these f such that, for some [...] satisfying p < [...].

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3 Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka