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

  • E. A. Sevost'yanov


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 $D$.
How to Cite
Sevost’yanov, E. 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, https://umj.imath.kiev.ua/index.php/umj/article/view/1693.
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