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  Volume 6, Issue 2, Article 34
On a Convolution Conjecture of Bounded Functions

    Authors: Krzysztof Piejko, Janusz Sokol, Jan Stankiewicz,  
    Keywords: Hadamard product, Convolution, Subordination, Bounded functions.  
    Date Received: 30/11/04  
    Date Accepted: 03/03/05  
    Subject Codes:

Primary 30C45; Secondary 30C55.

    Editors: Kazimierz Nikodem,  

We consider the convolution $ P(A,B)star P(C,D)$ of the classes of analytic functions subordinated to the homographies $ frac{1+Az}{1-Bz}$ and $ frac{1+Cz}{1-Dz}$ respectively, where $ A,B,C,D$ are some complex numbers. In 1988 J. Stankiewicz and Z. Stankiewicz [11] showed that for certain $ A,B,C,D$ there exist $ X,Y$ such that $ P(A,B)star P(C,D)subset P(X,Y)$. In this paper we verify the conjecture that $ P(X,Y)subset (A,B)star P(C,D)$ for some $ A,B,C,D,X,Y.$

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