Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $S(E).$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 30C45, 33C45

Retrieve articles in all journals with MSC (1991): 30C45, 33C45


Additional Information

E. Haliloglu
Email: halilogl@sariyer.cc.itu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01721-2
PII: S 0002-9947(97)01721-2
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