Convergence of the Sequence of Successive Approximations to a Fixed Point
Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
Fixed Point Theory and Applications 2010, 2010:716971 doi:10.1155/2010/716971Published: 2 February 2010
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.