On the equicontinuity of mappings with branching in the closure of the domain

  • E. A. Sevost'yanov

Abstract

We study the problem of local behavior of mappings f : D \rightarrow R^n,\; n \geq 2,$ in $D$. Under certain conditions imposed on a measurable function $Q(x), Q : D \rightarrow [0,\infty ]$, and the boundaries of $D$ and $D\prime = f(D)$, we show that a family of open discrete mappings $f : D \rightarrow R^n$ with a characteristic of quasiconformality $Q(x)$ is equicontinuous in $D$.
Published
25.02.2017
How to Cite
Sevost’yanovE. A. “On the Equicontinuity of Mappings With Branching in the Closure of the Domain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 2, Feb. 2017, pp. 273-9, http://umj.imath.kiev.ua/index.php/umj/article/view/1693.
Section
Short communications