Fixed Point Theory and Applications (Jan 2010)
Convergence of the Sequence of Successive Approximations to a Fixed Point
Abstract
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.