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Implicit iteration process with mean errors for common fixed points of a finite family of strictly pseudocontrative maps. (English) Zbl 1145.47053

The authors study weak and strong convergence of an implicit iteration with errors for finitely many strictly pseudo-contractive mappings in a Hilbert spaces. Recall that a mapping \(T\) from a subset \(K\) of a Hilbert space into \(K\) is strictly pseudo-contractive if there is \(0<k<1\) such that \(\| Tx-Ty\| ^2\leq\| x-y\| ^2+k\| (x-Tx)-(y-Ty)\| ^2\) for all \(x,y\in K\).

MSC:

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