An analogue of Koebe’s theorem and the openness of a limit map in one class

Abstract

We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe’s theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open.