Introduction

In this book we study approximate solutions of star-shaped feasibility problems in the presence of perturbations. A star-shaped problem is to find a point which belongs to the intersection of a given finite family of closed subsets of a Hilbert space which are star-shaped at a common point. Our goal is to show the convergence of algorithms, which are known as important tools for solving feasibility problems and common fixed point problems. Some of these algorithms are discussed is this chapter. We also discuss algorithms based on unions of nonexpansive maps, inconsistent convex feasibility problems and split common fixed point problems.