## 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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### References:

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