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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2004; 41(1): 145-156

Printed January 1, 2004

Copyright © The Korean Mathematical Society.

Holomorphic mappings into some domain in a complex normed space

Tatsuhiro Honda

Ariake National College of Technology

Abstract

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Let $D_1,D_2$ be convex domains in complex normed spaces $E_1$, $E_2$ respectively. When a mapping $f:D_1 \rightarrow D_2$ is holomorphic with $f(0)=0$, we obtain some results like the Schwarz lemma. Furthermore, we discuss a condition whereby $f$ is linear or injective or isometry.

Keywords: Schwarz lemma, complex geodesic

MSC numbers: 32F45, 32H02

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