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A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point
Author(s):
Tomonari
Suzuki
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4089-4093.
MSC (2000):
Primary 54H25
Posted:
June 4, 2008
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Abstract:
If  is a complete metric space and  is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of  starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader mappings.
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Additional Information:
Tomonari
Suzuki
Affiliation:
Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
Email:
suzuki-t@mns.kyutech.ac.jp
DOI:
10.1090/S0002-9939-08-09390-8
PII:
S 0002-9939(08)09390-8
Keywords:
Fixed point,
successive approximations,
Banach-Caccioppoli contraction principle,
Leader mapping
Received by editor(s):
August 20, 2007,
Received by editor(s) in revised form:
October 12, 2007
Posted:
June 4, 2008
Additional Notes:
The author was supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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