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

摘要

If (X, d) is a complete metric space and T : X --> 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.