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Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings. (English) Zbl 1127.47051

The main results of this paper are convergence theorems for approximating common fixed points of a finite family \(T_1,T_2,\dots,T_m\) of total asymptotically nonexpansive self-mappings by means of a multistep Mann type iterative scheme. It is also shown that all these results can be further extended to the case of total asymptotically non-self-mappings, using a corresponding projection type iterative scheme defined by a sunny nonexpansive retraction.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54H25 Fixed-point and coincidence theorems (topological aspects)
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