Research Article
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:10.1155/2010/716971
Published: 2 February 2010Abstract
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.
