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: letCbe a bounded closed convex subset of a Hilbert spaceE, and let{T(t):t∈ℝ+}be a strongly continuous semigroup of nonexpansive mappings onC. Fixu∈Candt1,t2∈ℝ+witht1<t2. Define a sequence{xn}inCbyxn=(1−αn)/(t2−t1)∫t1t2T(s)xnds+αnuforn∈ℕ, where{αn}is a sequence in(0,1)converging to0. Then{xn}converges strongly to a common fixed point of{T(t):t∈ℝ+}.