The set of common fixed points of a one-parameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt 2))

الأصل · EN

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.