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Properties of subordination chains and transition mappings in several complex variables

Curt Paula, Kohr Gabriela

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

11-18

Let B be the unit ball of Cn with respect to the Euclidean norm and f[z,t} be a Loewner chain. In this paper we study certain properties of f(z,t) and we obtain a sufficient condition for the transition mapping associated to f(z,t) to generate this chain.

The classes of functions which can be defined by subordination

Jurasińska R., Szpila A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

41-49

Let H = H(U) be the class of all functions which are holomorphic in the unit disc U = {z : \z\ < 1}. Let P(n) denotes the class of all functions p(z) = 1+piz+... is an element H, such thatp(pz) -< (1+zn/(1-zn), where -< denotes subordination. With the class P(n) we connect the subclass S*(n) of starlike functions in the following way. A function f(z) = z + a2z + ... belongs to S* (n) if and only if zf'(z)/f(z) is an element of P(n). In this note we give the estimations of some coefficients in the classes P(n) and S*(n) and we find the radius of convexity of the class S*(n).

Spirallike mappings on bounded balanced pseudoconvex domain in Cn

Hamada H., Kohr G.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

9-21

In this paper we will give some conditions of spirallikeness for holomorphic mappings defined on bounded balanced pseudoconvex domains in Cn with C1 plurisubharmonic defining functions.