Mappings slightly changing a fixed cross-ratio

Given a complex number λ ≠ 0, 1, we consider local homeomorphisms of a domain D ? ?? that, in a neighborhood of every point, change slightly (with a given smallness parameter δ) the cross-ratio of tetrads with fixed cross-ratio λ. We prove the quasiconformality of these mappings and obtain bounds for the coefficient of quasiconformality tending to 1 as δ → 0.