Coefficient bounds for analytic functions in an ellipse

Abstract

Let E-r be the elliptical domain E-r = { (x,y) is an element of R-2 : x(2) / (1+1/r(2))(2) + y(2)/(1-1/r(2))(2) < 1, r >1}. Let A(E-r) denote the analytic functions in E-r, also satisfying the normalization conditions F(0) = 0 and F' (0) = 1. In this paper, we obtain sharp bounds for the Faber coefficients of functions which belong to a certain subclass of A(E-r).