Strong convergence theorems for fixed points of asymptotically pseudocontractive semi-groups (Q1877790)

Let \(K\) be a (nonempty) closed bounded convex subset of a real Banach space \(E\) and \((T(t);t\geq 0)\) a strongly continuous uniformly asymptotically regular and uniformly Lipschitzian semigroup of asymptotically pseudocontractive selfmaps of \(K\). Sufficient conditions are given for the iterative sequence \((x_{n+1}:=(1-\lambda_n)x_n+\lambda_n (T(t_n))^nx_n- \lambda_n\theta_n(x_n-x_1);n\geq 1)\) to converge strongly to a fixed point of \((T(t);t\geq 0)\).