Equicontinuity of Families of Mappings with One Normalization Condition

We study the behavior of a certain class of mappings of a domain in Euclidean space. We prove that this class is equicontinuous both at the interior and boundary points, of the domain provided that it consists of mappings that satisfy a common normalization condition and whose quasiconformality characteristic has only tempered growth in a neighborhood of each point in the closure of the domain.