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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 ⋂ t≥0 F ( T (t) ) = F ( T (1) ) ∩ F ( T ( √ 2) ) holds. Using this theorem, we discuss convergence theorems to a common fixed point of {T (t) : t ≥ 0}.

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)