On equicontinuity of families of mappings with a fixed point of a domain

TL;DR

This paper investigates conditions under which families of mappings in Euclidean space are equicontinuous at boundary and interior points, focusing on normalization and quasiconformality characteristics.

Contribution

It establishes equicontinuity of mappings under normalization and weak quasiconformality growth conditions, extending understanding of boundary behavior.

Findings

Mappings are equicontinuous at boundary points under specified conditions

Equicontinuity holds at interior points with normalization and weak quasiconformality

Provides criteria linking quasiconformality characteristics to equicontinuity

Abstract

The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy the general normalization condition, and the corresponding characteristic of quasiconformality has a weak growth.