Approximate Solutions of Common Fixed-Point Problems

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§· dynamic§string-averaging version of the proximal algorithm§· common fixed§point problems in metric spaces§§· common fixed§point problems in the spaces with distances of the Bregman type§§· a proximal§algorithm for finding a common zero of a family of maximal monotone operators§§· subgradient§projections algorithms for convex feasibility problems in Hilbert spaces§