On equicontinuity of inverse mappings in a closure of a domain

TL;DR

This paper investigates the equicontinuity of inverse mappings of certain homeomorphisms satisfying upper modular estimates, proving their normality in the closure of a domain using prime ends.

Contribution

It establishes the equicontinuity (normality) of inverse mappings for a class of mappings with upper modular estimates in the prime ends framework.

Findings

Inverse mappings are equicontinuous in the closure of the domain.

Families of such homeomorphisms are normal.

The proof uses prime ends to analyze boundary behavior.

Abstract

For some class of mappings satisfying upper modular estimates with respect to families of curves, a behavior of the corresponding inverse mappings is investigated. In the terms of prime ends, it is proved that, families of such homeomorphisms are equicontinuous (normal) in the closure of a given domain.