Approximate Solutions of Common Fixed-Point Problems

Description

This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning  with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space Front Matter....Pages i-ix Introduction....Pages 1-11 Dynamic String-Averaging Methods in Hilbert Spaces....Pages 13-48 Iterative Methods in Metric Spaces....Pages 49-97 Dynamic String-Averaging Methods in Normed Spaces....Pages 99-151 Dynamic String-Maximum Methods in Metric Spaces....Pages 153-197 Spaces with Generalized Distances....Pages 199-250 Abstract Version of CARP Algorithm....Pages 251-288 Proximal Point Algorithm....Pages 289-318 Dynamic String-Averaging Proximal Point Algorithm....Pages 319-339 Convex Feasibility Problems....Pages 341-384 Iterative Subgradient Projection Algorithm....Pages 385-409 Dynamic String-Averaging Subgradient Projection Algorithm....Pages 411-446 Back Matter....Pages 447-454