Normal families of spaces mappings.
Ryazanov, V.I., Sevost'yanov, E.A. (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Ryazanov, V.I., Sevost'yanov, E.A. (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Dairbekov, N.S. (2000)
Siberian Mathematical Journal
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Piotr Hajłasz (1993)
Colloquium Mathematicae
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In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We...
Dariusz Partyka, Ken-ichi Sakan (2012)
Annales UMCS, Mathematica
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In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk D, if F(D) is a convex domain, then the inequality |G(z2)− G(z1)| < |H(z2) − H(z1)| holds for all distinct points z1, z2∈ D. Here H and G are holomorphic mappings in D determined by F = H + Ḡ, up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in ℂ and improve it...
Dairbekov, N.S. (2002)
Sibirskij Matematicheskij Zhurnal
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Turkoglu, Duran, Altun, Ishak, Fisher, Brian (2006)
Novi Sad Journal of Mathematics
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Greshnov, A.V. (2001)
Sibirskij Matematicheskij Zhurnal
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Dairbekov, N. S. (2000)
Sibirskij Matematicheskij Zhurnal
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Semenov, V. I. (2001)
Sibirskij Matematicheskij Zhurnal
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Pathak, Hemant Kumar, Tiwari, Rakesh (2011)
Banach Journal of Mathematical Analysis [electronic only]
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Samsonia, Z., Zivzivadze, L. (2002)
Georgian Mathematical Journal
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Rafiq, Arif, Acu, Ana Maria (2008)
Acta Universitatis Apulensis. Mathematics - Informatics
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Semenov, V.I. (2001)
Siberian Mathematical Journal
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