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Algebra i Analiz, 1997, Volume 9, Issue 3, Pages 198–204 (Mi aa788)  

Research Papers

On the Goodman conjecture and related functions of several complex variables

A. Z. Grinshpan

Department of Mathematics, University of South Florida, Tampa, FL
Abstract: The principal coefficient problem for $p$-valent functions, the Goodman conjecture, is considered for polynomial compositions. In this, case, the problem is reduced to a coefficient conjecture for functions of several complex variables related to univalent functions. The proof is based on the Lyzzaik–Styer determinant theorem. Some advantages of the equivalent conjecture are discussed.
Keywords: $p$-valent functions, the Goluzin area theorem, the Goodman conjecture.
Received: 03.01.1997
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. Z. Grinshpan, “On the Goodman conjecture and related functions of several complex variables”, Algebra i Analiz, 9:3 (1997), 198–204; St. Petersburg Math. J., 9:3 (1998), 595–600
Citation in format AMSBIB
\Bibitem{Gri97}
\by A.~Z.~Grinshpan
\paper On the Goodman conjecture and related functions of several complex variables
\jour Algebra i Analiz
\yr 1997
\vol 9
\issue 3
\pages 198--204
\mathnet{http://mi.mathnet.ru/aa788}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1466800}
\zmath{https://zbmath.org/?q=an:0901.32004}
\transl
\jour St. Petersburg Math. J.
\yr 1998
\vol 9
\issue 3
\pages 595--600
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    Алгебра и анализ St. Petersburg Mathematical Journal
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