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On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings. (English) Zbl 1086.47044
The authors study the weak and strong convergence of the implicit iteration sequences $\{ x_{n}\} $ defined by: $$\align x_{n}&= \alpha _{n}x_{n-1} + (1-\alpha _{n})T^{k(n)}_{i(n)}x_{n} + u_{n}, \quad n \geq 1\quad\text{and}\\ x_{n}&=\alpha _{n}x_{n-1} + (1- \alpha _{n})T^{k(n)}_{i(n)}x_{n},\quad n \geq 1\endalign$$ to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in real uniformly convex Banach spaces. Their results extend and improve results of several other authors.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
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