Strong Convergence of the Cq Method for Fixed Point Iteration Processes

  title={Strong Convergence of the Cq Method for Fixed Point Iteration Processes},
  author={Carlos Martinez and XU HONG-KUN},
(3) { zn = βnxn + (1− βn)Txn, xn+1 = αnxn + (1− αn)Tzn, n ≥ 0, where the initial guess x0 is taken arbitrarily and {αn}n=0 and {βn} are sequences in the interval [0, 1]. In general not much has been known regarding the convergence of the iteration processes (1)-(3) unless the underlying space X has nice properties which we briefly mention here. The iteration process (1) has been proved to be strongly convergent in both Hilbert spaces [7, 12, 24] and uniformly smooth Banach spaces [17, 20, 25… CONTINUE READING

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