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

Language: English

 English version: St. Petersburg Mathematical Journal, 1998, 9:3, 595–600

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