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

By Xiao-Tian Wang, Xiang-Qian Liang, Yu-lin Zhang. 2001

57 citations recorded by the source corpus.

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 C0H denote 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b5556ae0e30d493e2bd654eccd93d9df70ddb399

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Radius of close-to-convexity and fully starlikeness of harmonic mappings (2014, background): “7]), and the class of harmonic close-to-convex functions (see [4]).”
Planar harmonic univalent and related mappings. (2005, background): “Results of these types have been previously obtained only for functions in the special subclass CH ; see [69].”