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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the Faber coefficients
of functions univalent in an ellipse

Author: E. Haliloglu
Journal: Trans. Amer. Math. Soc. 349 (1997), 2901-2916
MSC (1991): Primary 30C45; Secondary 33C45
MathSciNet review: 1373635
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Abstract: Let $E$ be the elliptical domain

\begin{displaymath}E=\{x+iy: \frac {x^{2}}{(5/4)^{2}}+ \frac {y^{2}}{(3/4)^{2}}<1 \}.\end{displaymath}

Let $S(E)$ denote the class of functions $F(z)$ analytic and univalent in $E$ and satisfying the conditions $F(0)=0$ and $F'(0)=1$. In this paper, we obtain global sharp bounds for the Faber coefficients of the functions $F(z)$ in certain related classes and subclasses of $S(E).$

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E. Haliloglu

Keywords: Faber polynomials, Faber coefficients, Chebyshev polynomials, Jacobi elliptic sine function
Received by editor(s): October 17, 1994
Received by editor(s) in revised form: January 22, 1996
Article copyright: © Copyright 1997 American Mathematical Society