Bounds for certain linear combinations of the Faber coefficients of functions analytic in an ellipse
Künye
Haliloğlu, E. (2007). Bounds for certain linear combinations of the Faber coefficients of functions analytic in an ellipse. Proceedings of the Edinburgh Mathematical Society, 50(1), 163-171. doi:10.1017/S0013091504000574Özet
Let S? be a bounded, simply connected domain in C with 0 is an element of Omega and partial derivative Omega 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)}(n=0)(infinity) 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 [GRAPHICS] in terms of the Faber polynomials. Let where r > 1. In this paper, we obtain sharp bounds for certain linear combinations of the Faber coefficients of functions F(z) in S(E(r)) and in certain related classes.