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Stability and convergence of implicit iteration processes. (English) Zbl 1099.47524
Let \((X,d)\) be a metric space and \(T: X \times X \to X\) be an operator. The authors study the implicit iteration processes, \(x_n=T(x_n,x_{n-1})\), \(n \in \mathbb N\), for the solutions of the equation \(x=T(x,x)\).

MSC:
47J25 Iterative procedures involving nonlinear operators
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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