Explicit quasiconformal extensions for some classes of univalent functions

Mapping properties of nonlinear integral operators and pre-Schwarzian derivatives

“…Note that SS(α) ⊂ SS(1) = S * for 0 α 1. As is well known, for α ∈ (0, 1), each function f ∈ SS(α) is bounded (see [8]) and has a K(α)-quasiconformal extension to C, where K(α) = (1 + sin(απ/2))/(1 − sin(απ/2)) (see [12]). In particular, SS(α) ⊂ T 0 for α ∈ (0, 1).…”

Coefficient estimates and radii problems for certain classes of polyharmonic mappings

“…They are useful in studying questions of so-called δ-neighbourhoods originally considered by Ruscheweyh [34] (see also [35]) and in constructing explicit k-quasiconformal extensions of mappings (see Fait et al [36]). …”

Explicit quasiconformal extensions and Löwner chains

“…Let U 0 ðkÞ ¼ fw 2 C : jw À 1j kg for 0 k < 1. In [4], they have shown that for f 2 A, if f 0 ðzÞ 2 U 0 ðkÞ then f has a k-quasiconformal extension by giving the explicit extension fðwÞ ¼ fðwÞ;…”