2006•Taiwanese Journal of MathematicsRequires access
THE SET OF COMMON FIXED POINTS OF A ONE-PARAMETER CONTINUOUS SEMIGROUP OF NONEXPANSIVE MAPPINGS IS F IN STRICTLY CONVEX BANACH SPACES
Tomonari Suzuki
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Abstract
In this paper, we prove the following. Let E be a strictly convex
Banach space. Let {T(t) : t ≥ 0} be a one-parameter strongly continuous
semigroup of nonexpansive mappings on a subset C of E. Then
t≥0
F
T(t)
= F
1
2T(1) +
1
2T(
√
2)
holds, where F
T(t)
is the set of fixed points of T(t) for each t ≥ 0.