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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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