Precise Coefficient Estimates for Close-to-Convex Harmonic Univalent Mappings

The class SH consists of harmonic, univalent, and sense-preserving functions f in the open unit disk U = z z < 1 , such that f = h + ¯g, where h z = z + ∞ n=2 anzn and g z = ∞ n=1 a −nzn. Let S0H , CH, and C0Hdenote the subclass of SH with a −1 = 0, the subclass of SH with f being a close-to-convex mapping, and the intersection of S0H and CH, respectively. In this paper, for f ∈ C0H and f ∈ CH, we prove that the harmonic analogue of the Bieberbach conjecture and the generalization of the Bieberbach conjecture are true