## Weak and strong convergence of a scheme with errors for two nonexpansive mappings.(English)Zbl 1086.47050

Let $$C$$ be a (nonempty) bounded closed convex subset of a Banach space $$E$$ and $$(S,T)$$ be a pair of asymptotically nonexpansive selfmaps of $$C$$. The weak and strong convergence of the iterative scheme $$x_{n+1}=a_nSy_n+b_nx_n+c_nu_n,$$ $$y_n=a'_nTx_n+b'_nx_n+c'_nv_n$$ $$(n\geq 1)$$ is discussed; here, $$(a_n)$$, $$(b_n)$$ $$(c_n)$$, $$(a'_n)$$, $$(b'_n)$$, $$(c'_n)$$ are sequences in $$[0,1]$$ with certain regularity properties and $$(u_n)$$, $$(v_n)$$ are bounded sequences in $$C$$.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 49M05 Numerical methods based on necessary conditions 65J15 Numerical solutions to equations with nonlinear operators
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### References:

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