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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)