*Bull. Austral. Math. Soc.* 72(3) pp.371--379, 2005.

# A strong convergence theorem for contraction semigroups in Banach spaces

## Hong-Kun Xu |

Supported in part by the National Research Foundation of South Africa.

## Abstract

We establish a Banach space version of a
theorem of Suzuki . More precisely we prove that if
for all

*X*is a uniformly convex Banach space with a weakly continuous duality map (for example,*l*^{p}for 1 <*p*< ), if*C*is a closed convex subset of*X*, and if =*T*(*t*) :*t*0 is a contraction semigroup on*C*such that Fix() , then under certain appropriate assumptions made on the sequences {} and {*t*_{n}} of the parameters, we show that the sequence {*x*_{n}} implicitly defined by*x*

_{n}=

*u*+ (1 - )

*T*(

*t*

_{n})

*x*

_{n}

*n*1 converges strongly to a member of Fix().#### Click to download PDF of this article (free access until July 2006)

#### or get the *no-frills*
version

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(Metadata: XML, RSS, BibTeX) | MathSciNet: MR2199638 | Z'blatt-MATH: 1095.47016 |

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ISSN 0004-9727