A strong convergence theorem for contraction semigroups in Banach spaces

By Hong-Kun Xu. Bulletin of the Australian Mathematical Society, 2005

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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).

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

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