On the coefficient problem for univalent functions

V. G. Sheretov

Tver State University

Abstract: We prove a criterion for analytic functions to belong to the classes $S^{(p)}$ and $\Sigma^{(p)}$ of univalent functions with $p$-multiple circular symmetry in terms of countable systems of exact coefficient inequalities. As a consequence we obtain a description for the corresponding domains of coefficients.

UDC: 517.54

Received: 17.06.2001

 English version: Siberian Mathematical Journal, 2002, 43:2, 379–387

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