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A new characterization of Möbius transformations by use of Apollonius hexagons
Authors:
Hiroshi Haruki and Themistocles M. Rassias
Journal:
Proc. Amer. Math. Soc. 128 (2000), 2105-2109
MSC (1991):
Primary 39B40; Secondary 33A70
Posted:
February 25, 2000
MathSciNet review:
1653398
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Abstract: The purpose of this paper is to give a new characterization of Möbius transformations from the standpoint of conformal mappings. To this end a new concept of Apollonius hexagons on the complex plane is used.
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H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, Random House, New York, 1967.
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A. Fuchs and B.
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applications. Vol. I, Original translation by J. Berry; revised and
expanded by J. W. Reed, Pergamon Press, Oxford, 1964. MR 0160878
(28 #4087)
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H. Haruki and Th. M. Rassias, A new characteristic of Möbius transformations by use of Apollonius quadrilaterals, Proc. Amer. Math. Soc. 126 (10) (1998), 2857-2861. CMP 99:04
- 4.
Hiroshi
Haruki, A proof of the principle of circle-transformation by the
use of a theorem on univalent functions, Enseignement Math. (2)
18 (1972), 145–146. MR 0325966
(48 #4312)
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S. Rabinowitz (ed.), Index to Mathematical Problems 1980-1984, MathPro Press, 1992.
- 1.
- H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, Random House, New York, 1967.
- 2.
- B. A. Fuchs and B. V. Shabat, Functions of a Complex Variable I, Pergamon Press, 1964. MR 28:4087
- 3.
- H. Haruki and Th. M. Rassias, A new characteristic of Möbius transformations by use of Apollonius quadrilaterals, Proc. Amer. Math. Soc. 126 (10) (1998), 2857-2861. CMP 99:04
- 4.
- H. Haruki, A proof of the principle of circle-transformation by the use of a theorem on univalent functions, L'Enseignement Mathematique 18 (2) (1972), 145-146. MR 48:4312
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- S. Rabinowitz (ed.), Index to Mathematical Problems 1980-1984, MathPro Press, 1992.
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Additional Information
Hiroshi Haruki
Affiliation:
Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Themistocles M. Rassias
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece
Email:
trassias@math.ntua.gr
DOI:
http://dx.doi.org/10.1090/S0002-9939-00-05246-1
PII:
S 0002-9939(00)05246-1
Keywords:
M\"obius transformations,
conformal mapping,
Apollonius hexagons
Posted:
February 25, 2000
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000 American Mathematical Society
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