Abstract and Applied Analysis
Volume 2006 (2006), Article ID 58684, 10 pages
doi:10.1155/AAA/2006/58684

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

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∈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 xn=(1−αn)/(t2−t1)∫t1t2T(s)xnds+αnu 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+}.