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A strong convergence theorem for contraction semigroups in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Hong-Kun Xu
Hong-Kun Xu
Affiliation:
School of Mathematical Sciences University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa e-mail: xuhk@ukzn.ac.za
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We establish a Banach space version of a theorem of Suzuki [8]. More precisely we prove that if X is a uniformly convex Banach space with a weakly continuous duality map (for example, lp for 1 < p < ∞), if C is a closed convex subset of X, and if F = {T (t): t ≥ 0} is a contraction semigroup on C such that Fix(F) ≠ ∅, then under certain appropriate assumptions made on the sequences {αn} and {tn} of the parameters, we show that the sequence {xn} implicitly defined by

for all n ≥ 1 converges strongly to a member of Fix(F).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 371 - 379
Copyright
Copyright © Australian Mathematical Society 2005

References

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