Solutions of Fixed Point Problems with Computational Errors (Springer Optimization and Its Applications, 210)

Preface
Contents
1 Introduction
	Star-Shaped Feasibility Problems
	Algorithms Based on Unions of Nonexpansive Maps
	Inconsistent Convex Feasibility Problems
	Split Common Fixed Point Problems
2 Iterative Methods in a Hilbert space
	Preliminaries
	Exact Iterates
	Inexact Iterates with Summable Errors
	The First Result with Nonsummable Errors
	The Second Result with Nonsummable Errors
	The Third Result with Nonsummable Errors
	Almost Star-Shaped Feasibility Problems
3 The Cimmino Algorithm in a Hilbert Space
	Exact Cimmino Iterates
	Inexact Cimmino Iterates with Summable Errors
	The First Result with Nonsummable Errors for the Cimmino Algorithm
	The Second Result with Nonsummable Errors for the Cimmino Algorithm
	The Third Result with Nonsummable Errors for the Cimmino Algorithm
	The Cimmino Algorithm for Almost Star-Shaped Feasibility Problems
4 Dynamic String-Averaging Methods in Hilbert Spaces
	Preliminaries
	Exact Iterates
	Inexact Iterates with Summable Errors
	The First Result with Nonsummable Errors
	The Second Result with Nonsummable Errors
	The Third Result with Nonsummable Errors
	Almost Star-Shaped Feasibility Problems
5 Methods with Remotest Set Control in a Hilbert Space
	Exact Iterates
	Inexact Iterates with Summable Errors
	The First Result with Nonsummable Errors
	The Second Result with Nonsummable Errors
	The Third Result with Nonsummable Errors
	Almost Star-Shaped Feasibility Problems
6 Algorithms Based on Unions of Nonexpansive Maps
	Global Convergence of Iterates
	An Auxiliary Result
	Proof of Theorem 6.1
	Proof of Theorem 6.2
	Krasnosel\'ski-Mann Iterations
	Proof of Theorem 6.4
	Proof of Theorem 6.5
	The Cimmino Type Algorithm
	Proof of Theorem 6.6
	Proof of Theorem 6.7
	Global Convergence of Iterates with Summable Errors
	Proof of Theorem 6.8
	Proof of Theorem 6.9
	The Cimmino Algorithm with Summable Errors
	Iterates with Nonsummable Errors
	Auxiliary Results for Theorem 6.15
	The Cimmino Algorithm with Nonsummable Errors
	Auxiliary Results for Theorem 6.23
	Proof of Theorem 6.23
	The Behavior of Iterates Without Compactness Assumptions
	Inexact Iterates Without Compactness Assumptions
	Extensions
7 Inconsistent Convex Feasibility Problems
	Preliminaries
	Main Results
	An Auxiliary Result
	Proof of Theorem 7.2
	Proof of Theorem 7.3
8 Split Common Fixed Point Problems
	Preliminaries
	The Main Result
	Proof of Theorem 8.2
	The Split Common Fixed Point Problem with Several Maps
	Proof of Theorem 8.4
References
Index