Abstract

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+} be a strongly continuous semigroup of nonexpansive mappings on C. Fix uC and t1,t2+ with t1<t2. Define a sequence {xn} in C by xn=(1αn)/(t2t1)t1t2T(s)xnds+αnu for 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+}.