General iteration algorithm and convergence rate optimal model for common fixed points of nonexpansive mappings (Q878942)

Let there be a finite set of nonexpansive operators mapping a closed convex subset of a real uniformly convex Banach space into itself. The Banach space is supposed to fulfill Opial's condition, i.e. if \((x_n)\) converges weakly towards \(x\) then \(\limsup \|x_n-x\| < \limsup \|x_n - y\|\) for all \(y\neq x\). The set of operators is supposed to possess a common fixed point. The authors prove weak and -- under an additional assumption -- strong convergence of a general implicit composite iteration towards a common fixed point. The Mann iteration is a special case of this general iteration. Finally, the authors study the optimal choice of the iteration parameters and the rate of convergence.