Geodesic
A Variation of the Koebe Mapping in a Dense Subset of S
Canadian journal of mathematics, Tome 39 (1987) no. 1, pp. 54-73

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Let H(U) be the linear space of holomorphic functions defined on the unit disk U endowed with the topology of normal (locally uniform) convergence. For a subset E ⊂ H(U) we denote by Ē the closure of E with respect to the above topology. The topological dual space of H(U) is denoted by H′(U).Let D, 0 ∊ D, be a simply connected domain in C. The unique univalent conformal mapping φ from U onto D, normalized by φ(0) = 0 and φ′(0) > 0 will be called “the Riemann Mapping onto D”. Let S be the set of all normalized univalent functions 
Bshouty, D.; Hengartner, W. A Variation of the Koebe Mapping in a Dense Subset of S. Canadian journal of mathematics, Tome 39 (1987) no. 1, pp. 54-73. doi: 10.4153/CJM-1987-004-8
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