Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
- Suzuki, Tomonari
Publication date
May 2005
DOI Publisher
Elsevier Inc. ISSN
0022-247X Citation count (estimate)
530Abstract
AbstractIn this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let {T(t):t⩾0} be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {tn} be a sequence in [0,∞) satisfying lim infn→∞tn<lim supn→∞tnandlimn→∞(tn+1−tn)=0. Let λ∈(0,1). Define a sequence {xn} in C by x1∈C and xn+1=λT(tn)xn+(1−λ)xn for n∈N. Then {xn} converges strongly to a common fixed point of {T(t):t⩾0}
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