Stability and convergence of implicit iteration processes. (English) Zbl 1099.47524

Pham Ky Anh; Tran Quoc Binh

Vietnam J. Math. 32, No. 4, 467-473 (2004).

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 \(x=T(x,x)\).

Reviewer: Ioan A. Rus (Cluj-Napoca)

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)

Keywords:

fixed point; implicit iteration processes; global convergence; local convergence