Common fixed points of one‐parameter nonexpansive semigroups in strictly convex Banach spaces

One of our main results is the following convergence theorem for one‐parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t) : t ∈ ℝ+} be a strongly continuous semigroup of nonexpansive mappings on C. Fix u ∈ C and t1, t2 ∈ ℝ+ with t1 < t2. Define a sequence {xn} in C by for n ∈ ℕ, where {αn} is a sequence in (0, 1) converging to 0. Then {xn} converges strongly to a common fixed point of {T(t) : t ∈ ℝ+}.