Coefficient inequalities for concave and meromorphically starlike univalent functions

Abstract

Let D denote the open unit disk and f : D ! C be mero- morphic and univalent in D with the simple pole at p 2 (0,1) and satis- fying the standard normalization f(0) = f 0 (0) − 1 = 0. Also, let f have the expansion f(z) = 1 X n=−1 an(z − p) n , jz − pj< 1 − p, such that f maps D onto a domain whose complement with respect to C is a convex set (starlike set with respect to a point w0 2 C,w0 6 0 resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by Co(p) (� s (p,w0) resp.). We prove some coefficient estimates for functions in the classes where the sharpness of these estimates is also achieved.