On equicontinuity of mappings in a case of variable domains

Abstract

We study a local behavior of one class of mappings, which are defined in a domain of $n$-measured Euclidean space, in a case, when corresponding images of this domain are variable. Under some conditions on a function defining a behavior of mappings mentioned above, and some restrictions on mapped domains, the equicontinuity of the corresponding family of the mappings in the closure of the initial domain is proved.