The set of common fixed points of a one-parameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt 2))
Tomonari Suzuki
Abstract
In this paper, we prove the following theorem: Let T(t) : t >= 0 be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T(t) is denoted by F(T(t)) for each t >= 0. Then capt >= 0 F(T(t)) = F(T(1)) cap F(T(sqrt 2)) holds. Using this theorem, we discuss convergence theorems to a common fixed point of T(t) : t >= 0.
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