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Bounds for the faber coefficients of certain classes of functions analytic in an ellipse

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Date

2005

Author

Haliloğlu, Engin
Johnston, Elgin H.

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Citation

Haliloglu, E., & Johnston, E. H. (2005). Bounds for the faber coefficients of certain classes of functions analytic in an ellipse. Rocky Mountain Journal of Mathematics, 35(1), 167-179.

Abstract

Let Omega be a bounded, simply connected domain in C with 0 is an element of Omega and aOmega analytic. Let S(Omega) denote the class of functions F(z) which are analytic and univalent in Omega with F(0) = 0 and F'(0) = 1. Let {Phi(n)(z)} infinity n=0 be the Faber polynomials associated with Omega. If F(z) is an element of S(Omega), then F(z) can be expanded in a series of the form where r > 1. In this paper we obtain sharp bounds for the Faber coefficients A(0), A(1) and A(2) of functions F(z) in S(E-r) and in certain related classes.

Volume

35

Issue

1

URI

https://hdl.handle.net/11729/196
http://dx.doi.org/10.1216/rmjm/1181069774

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  • İİBF - Makale Koleksiyonu | İşletme Bölümü / Department of Management [36]
  • Makale Koleksiyonu [797]
  • Makale Koleksiyonu [704]



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