Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings
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 \(x_{n+1}=(1-a_n)x_n+a_nS^ny_n+u_n,\) \(y_n=(1-b_n)x_n+b_nT^nx_n+v_n\) \((n\geq 1)\) is discussed; here, \((a_n)\), \((b_n)\) are sequences in \([0,1]\) and \((u_n)\), \((v_n)\) are sequences in \(E\) with \(\sum_n u_n, \sum_n v_n < \infty\).
scientific article; zbMATH DE number 2171565