## A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point

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**136**(2008), 4089-4093 Request permission

## Abstract:

If $(X, d)$ is a complete metric space and $T : X \to X$ is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of $T$ 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.## References

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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
- Received by editor(s): August 20, 2007
- Received by editor(s) in revised form: October 12, 2007
- Published electronically: 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 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**136**(2008), 4089-4093 - MSC (2000): Primary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-08-09390-8
- MathSciNet review: 2425751