**Weak convergence theorems for strongly continuous semigroups of pseudocontractions**

* Duong Viet Thong
*

**Abstract**

Let *K*be a nonempty closed convex subset of a uniformly convex Banach space

*E*, let {

*T*(

*t*):

*t*≥0} be a strongly continuous semigroup of nonexpansive mappings from

*K*into itself such that

*F*:=⋂

_{ t≥0}

*F*(

*T*(

*t*))≠∅. Assuming that {

*α*

_{ n }} and {

*t*

_{ n }} are sequences of real numbers satisfying appropriate conditions, we show that the sequence {

*x*

_{ n }} defined by

*F*. This extends Thong’s result (Thong, Nonlinear Anal. 74, 6116–6120, 2011) from a Hilbert space setting to a Banach space setting. Next, theorems of weak convergence of an implicit iterative algorithm with errors for treating a strongly continuous semigroup of Lipschitz pseudocontractions are established in the framework of a real Banach space.