Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
Academic Editor: Mohamed A. Khamsi
Copyright © 2010 Tomonari Suzuki. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
If is a complete metric space and is a contraction on , then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of
successive approximations of starting from any point converges to a unique fixed point. In this paper, using the concept of -distance, we obtain simple, sufficient, and necessary conditions of the above conclusion.