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Approximating common fixed points of two asymptotically nonexpansive mappings. (English) Zbl 0985.47042

Let \(E\) be a Banach space; \(C\) a nonempty bounded closed convex subset of \(E\). For a pair \(S,T: C \rightarrow C\) of asymptotically nonexpansive maps [see the review above on the paper by T. Domínguez-Benavides and P. Lorenzo Ramírez, Proc. Am. Math. Soc. 129, No. 12, 3549-3557 (2001; Zbl 0985.47040)] the authors study weak and strong convergence of the iterative procedure \[ x_{n+1} = (1-a_n)x_n + a_nS^n[(1-b_n)x_n + b_nT^nx_n] \] where \(0 \leq a_n \leq 1\), \(0 \leq b_n \leq 1\) to the common fixed points of \(S\) and \(T\).

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
49M05 Numerical methods based on necessary conditions
47H10 Fixed-point theorems

Citations:

Zbl 0985.47040
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