Coefficient inequalities for concave and meromorphically starlike univalent functions

Abstract

Abstract. Let D denote the open unit disk and f: D → C be meromorphic and univalent in D with a simple pole at p ∈ (0, 1) and satisfying the standard normalization f(0) = f′(0)-1 = 0. Also, assume that f has the expansion, and maps D onto a domain whose complement with respect to C is a convex set (starlike set with respect to a point w 0 ∈ C, w 0 ≠ = 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by Co(p) (σ s(p, w 0) resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established. © Instytut Matematyczny PAN, 2008.