✦ LIBER ✦
Precise Coefficient Estimates for Close-to-Convex Harmonic Univalent Mappings
✍ Scribed by Xiao-Tian Wang; Xiang-Qian Liang; Yu-Lin Zhang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 89 KB
- Volume
- 263
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
The class S H consists of harmonic, univalent, and sense-preserving functions f in the open unit disk U = z z < 1 , such that f = h + ḡ, where h z = z + ∞ n=2 a n z n and g z = ∞ n=1 a -n z n . Let S 0 H , C H , and C 0 H denote the subclass of S H with a -1 = 0, the subclass of S H with f being a close-to-convex mapping, and the intersection of S 0 H and C H , respectively. In this paper, for f ∈ C 0 H and f ∈ C H , we prove that the harmonic analogue of the Bieberbach conjecture and the generalization of the Bieberbach conjecture are true.