# On equicontinuity of mappings in a case of variable domains

## TL;DR

This paper investigates the equicontinuity of a class of mappings in variable domains within Euclidean space, establishing conditions under which these mappings are uniformly continuous on the domain closure.

## Contribution

It provides new conditions on the defining functions and domain restrictions that guarantee equicontinuity of mappings with variable images in Euclidean space.

## Key findings

- Established conditions for equicontinuity of mappings in variable domains.
- Proved equicontinuity in the closure of the initial domain under specified conditions.
- Extended understanding of mapping behavior in variable domain settings.

## 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.