## 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

Zbl 0985.47040