Majoration de la norme des facteurs d'un polynôme
Here we investigate a majorization problem involving starlike meromorphic functions of complex order belonging to a certain subclass of meromorphic univalent functions defined by an integral operator introduced recently by Lashin.
In this paper we consider the extensions of quasiconformal mappings f: B → Ωs to the whole plane, when the domain Ωs is a domain with a cusp of degree s > 0 and thus not an quasidisc. While these mappings do not have quasiconformal extensions, they may have extensions that are homeomorphic mappings of finite distortion with an exponentially integrable distortion, but in such a case ∫2B exp(λK(x)) dx = ∞ for all λ > 1/s. Conversely, for a given s > 0 such a mapping is constructed...
We establish continuity, openness and discreteness, and the condition (N) for mappings of finite distortion under minimal integrability assumptions on the distortion.