On boundary behavior of mappings with two normalized conditions 

Author 
esevostyanov2009@gmail.com^{1},
1) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine; 2) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine; 3) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine

Abstract 
The paper is devoted to a study of mappings with finite distortion that have been recently
actively investigated last time. We study the boundary behavior of mappings between two fixed
domains in metric spaces, which satisfy some moduli estimates. We have proved that families
of corresponding inverse mappings with two normalized conditions and integrable majorant are
equicontinuous whenever the domain of the mappings has a weakly
at boundary

Keywords 
metric spaces; quasiconformal mappings; mappings with bounded and finite distortion; equicontinuity;
moduli of families of paths

DOI 
doi:10.15330/ms.49.2.150157

Reference 
1. E. A. Sevost’yanov, S. A. Skvortsov, On convergence of mappings in metric spaces with direct and inverse
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2. O. Martio, V. Ryazanov, U. Srebro and E. Yakubov, Moduli in Modern Mapping Theory, Springer Monographs in Mathematics, Springer, New York etc., 2009. 3. V. Ryazanov, R. Salimov, Weakly flat spaces and boundaries in the mapping theory, Ukr. Math. Visnyk, 4 (2007), ¹2, 199–233 (in Russian); translation in Ukr. Math. Bull., 4 (2007), ¹2, 199–233. 4. E. S. Smolovaya, Boundary behavior of ring Qhomeomorphisms in metric spaces, Ukr. Mat. Zh., 62 (2010), ¹5, 682–689 (in Russian); translation in Ukr. Math. Journ., 62 (2010), ¹5, 785–793. 5. K. Kuratowski, Topology, V.2, Academic Press, New York–London, 1968. 6. E. A. Sevost’yanov, On local and boundary behavior of mappings in metric spaces, Algebra and analiz 28 (2016), ¹6, 118–146; translation Local and boundary behavior of maps in metric spaces, St. Petersburg Math. J., 28 (2017), ¹6, 807–824. 7. M. Vuorinen, On the existence of angular limits of ndimensional quasiconformal mappings, Ark. Mat., 18 (1980), 157–180. 8. E. A. Sevost’yanov, R. R. Salimov, On inner dilatations of the mappings with unbounded characteristic, Ukr. Mat. Visnyk, 8 (2011), ¹1, 129–143 (in Russian); translation in J. Math. Sci. (N. Y.), 178 (2011), ¹1, 97–107. 
Pages 
150157

Volume 
49

Issue 
2

Year 
2018

Journal 
Matematychni Studii

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