Stable iteration procedures in metric spaces which generalize a Picard-type iteration
Let \((X,d)\) be a complete metric space and \(f, T\) be self-mappings of \(X\). The Picard iteration \(x_{k+1}=f(Tx_k)\) is said to be \(T\)-stable if for any \(x_0\in X\) the sequence \(\{x_k\}\) converges to a fixed point of \(fT\), whenever \(\lim_{k\rightarrow \infty}d(x_{k+1}, Tx_k)=0\). By using the concepts of altering-distance function and extended altering-distance function, the author obtains generalizations of some results concerning the \(T\)-stability of the iterations.
scientific article; zbMATH DE number 5792465
scientific article