Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new characteristic of Möbius
transformations by use of
Apollonius quadrilaterals

Authors: Hiroshi Haruki and Themistocles M. Rassias
Journal: Proc. Amer. Math. Soc. 126 (1998), 2857-2861
MSC (1991): Primary 32A20
MathSciNet review: 1485479
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to give a new invariant characteristic property of Möbius transformations from the standpoint of conformal mapping. To this end a new concept of ``Apollonius quadrilaterals'' is used.

References [Enhancements On Off] (What's this?)

  • 1. J. Aczél and M. A. McKiernan, On the characterization of plane projective and complex Möbius transformation, Math. Nachr. 33 (1967), 315-337. MR 36:5806
  • 2. J. Aczél, Functional equations and L'Hôpital's rule in an exact Poisson derivation, Amer. Math. Monthly 97 (1990), 423-426. CMP 9:11
  • 3. H. S. M. Coxeter, Introduction to Geometry (5th ed.), John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 23:A1251
  • 4. H. Haruki, A proof of the principle of circle-transformation by use of a theorem on univalent functions, L'Enseignement Mathématique 18 (1972), 145-146. MR 48:4312
  • 5. H. Haruki and Th. M. Rassias, A new invariant characteristic property of Möbius transformations from the standpoint of conformal mapping, Journal of Mathematical Analysis and Applications 181 (1994), 320-327. MR 94m:30018
  • 6. E. A. Maxwell, Geometry for Advanced Pupils, Oxford University Press, 1957.
  • 7. Z. Nehari, Conformal Mapping, McGraw-Hill Book Co., New York, 1952. MR 13:640h
  • 8. R. Nevanlinna and V. Paatero, Introduction to Complex Analysis, Addison-Wesley, New York, 1964. MR 39:415
  • 9. L. L. Pennisi, L. I. Gordon and S. Lasher, Elements of Complex Variables, Holt, Rinehart and Winston, New York, 1963.
  • 10. E. C. Titchmarsh, The Theory of Functions (2nd ed.), Clarendon Press, Oxford, 1939.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32A20

Retrieve articles in all journals with MSC (1991): 32A20

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

Received by editor(s): February 18, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society