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Univalent σ-Harmonic Mappings

✍ Scribed by Giovanni Alessandrini; Vincenzo Nesi

Publisher
Springer
Year
2001
Tongue
English
Weight
124 KB
Volume
158
Category
Article
ISSN
0003-9527

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✍ Xiao-Tian Wang; Xiang-Qian Liang; Yu-Lin Zhang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 89 KB

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 c

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✍ W. Majchrzak 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 174 KB

A class of harmonic univalent mappings is constructed by applying the method of Clunie and Sheil-Small. These mappings, assuming their values in a half-plane with a vertical boundary, omit two vertical half-lines symmetric w.r.t. the real axis. Several basic properties are proved.