Proceedings of the American Mathematical Society

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The set of common fixed points of a one-parameter continuous semigroup of mappings is $F \big( T(1) \big) \cap F \big( T(\sqrt2) \big)$

Author: Tomonari Suzuki
Journal: Proc. Amer. Math. Soc. 134 (2006), 673-681
MSC (2000): Primary 47H20, 47H10
Posted: September 28, 2005
MathSciNet review: 2180883
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Abstract: In this paper we prove the following theorem: Let $\{ T(t) : t \geq 0 \}$ be a one-parameter continuous semigroup of mappings on a subset of a Banach space . The set of all fixed points of is denoted by $F \big( T(t) \big)$ for each $t \geq 0$ . Then

$\displaystyle \bigcap_{t \geq 0} F \big( T(t) \big) = F \big( T(1) \big) \cap F \big( T(\sqrt 2) \big)$

holds. Using this theorem, we discuss convergence theorems to a common fixed point of $\{ T(t) : t \geq 0 \}$ .

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