2006•Proceedings of the American Mathematical SocietyRequires access
The set of common fixed points of a one-parameter continuous semigroup of mappings is f(t(1))∩f(t(√2))
Tomonari Suzuki
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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 all fixed points of T(t) is denoted by F(T(t)) for each t > 0. Then ∩ F(T(t)) = F(T(1)) n F(T(√2)) t>0 holds. Using this theorem, we discuss convergence theorems to a common fixed point of {T(t): t > 0}.