Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings. (English) Zbl 1105.47061

In this paper, a new implicit iteration scheme with perturbed mapping for the approximation of common fixed points of a finite family of nonexpansive mappings is given. Some convergence theorems and necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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