Strong convergence theorems for strongly continuous semigroups of pseudocontractions (Q654199)

Let \(E\) be a Banach space and \(K\) be a closed convex subset of \(E\). Let \((T(t): t\geq 0)\) be a strongly continuous semigroup of Lipschitz pseudocontractions from \(K\) to itself with \(F:=\bigcap\{\text{Fix}(T(t)): t\geq 0\}\neq \emptyset\). The strong convergence of the implicit iterative process \[ x_0\in K,\;x_{n}=\alpha_nx_{n-1}+\beta_nT(t_n)x_n+\gamma_ne_n,\;n\geq 1 \] towards an element of \(F\) is discussed, under mild conditions upon these data.