In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the -convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the s...

Contents Chapter 1. Martingales, continued 1 1.1. Martingales indexed by partially ordered sets 1 1.2. Notions of convergence for martingales 3 1.3. Uniform integrability 4 1.4. Convergence of martingales with directed index sets 6 1.5. Application: The 0-1 law of Kolmogorov 8 1.6. Continuous-time martingales 9 1.7. Tail bounds for martingales 12 1.8. Application: The Pólya urn 13 1.9. Applicat...