A characterization of the convergence of Picard iteration to a fixed point for a continuous mapping and an application (Q2571977)

Some characteristic conditions are introduced for the convergence of Picard iterations \((T^n(x_0))\) to a fixed point of a continuous map \(T:D\subseteq X \to X\). As an application, the convergence of Ishikawa iterations \((T^n_{\lambda, \mu}(x_0))\) towards the fixed point of the nonexpansive map \(T:D\subseteq X\to X\) is established.