The set of common fixed points of a one-parameter continuous semigroup of mappings is 𝐹\big(𝑇(1)\big)∩𝐹\big(𝑇(√2)\big)

In this paper we prove the following theorem: Let { T ( t ) : t ≥ 0 } \{ T(t) : t \geq 0 \} be a one-parameter continuous semigroup of mappings on a subset C C of a Banach space E E . The set of all fixed points of T ( t ) T(t) is denoted by F ( T ( t ) ) F \big ( T(t) \big ) for each t ≥ 0 t \geq 0 . Then \[ ⋂ t ≥ 0 F ( T ( t ) ) = F ( T ( 1 ) ) ∩ F ( T ( 2 ) ) \bigcap _{t \geq 0} F \big ( T(t) \big ) = F \big ( T(1) \big ) \cap F \big ( T(\sqrt 2) \big ) \] holds. Using this theorem, we discuss convergence theorems to a common fixed point of