@article {Xu2005,
 author="Hong-Kun Xu",
 title={A strong convergence theorem for contraction semigroups in Banach spaces},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="3",
 pages="371--379",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="19th May, 2005",
 classmath="47H20, 47H09",
 publisher={AMPAI, Australian Mathematical Society},
 url="http://www.austms.org.au/Publ/Bulletin/V72P3/723-5157-Xu/index.shtml",
 acknowledgement={Supported in part by the National Research Foundation of South Africa.},
 abstract={ We establish a Banach space version of a theorem of Suzuki \cite {Su}. More precisely we prove that if $X$ is a uniformly convex Banach space with a weakly continuous duality map (for example, $l^p$ for $1<p<\infty $), if $C$ is a closed convex subset of $X$, and if $\mathcal {F}=\bigl \{T(t):t\ge 0\bigr \}$ is a contraction semigroup on $C$ such that $\Fix (\mathcal {F})\not =\emptyset $, then under certain appropriate assumptions made on the sequences $\{\alpha _n\}$ and $\{t_n\}$ of the parameters, we show that the sequence $\{x_n\}$ implicitly defined by $$x_n=\alpha _n u+(1-\alpha _n)T(t_n)x_n$$ for all $n\ge 1$ converges strongly to a member of $\Fix (\mathcal {F})$. }
}