Algorithms for solving common fixed point problems
type: Item
instance of: scholarly article
title: Algorithms for solving common fixed point problems
zbMATH Open document ID: 1447.47012
DOI: 10.1007/978-3-319-77437-4
published in: Springer Optimization and Its Applications
publication date: 2018-04-05T00:00:00Z
review text: In this textbook, the author studies approximate solutions of common fixed point and convex feasibility problems in the presence of perturbations. In order to to serve the purpose, he considers a number of algorithms, which are known as important tools for the purpose. The author discusses both summable perturbations and nonsummable perturbations. The book contains eight chapters. Chapter 1 is an introduction. In Chapter~2, iterative methods in metric spaces are studied. The dynamic string-averaging methods for common fixed point problems in normed spaces are analysed in Chapter~3. Dynamic string methods for common fixed point problems in a metric space are introduced and studied in Chapter~4. Chapter~5 is devoted to the study of the convergence of an abstract version of the algorithm which is known in the literature as component averaged row projections or CARP. In Chapter~6, the author addresses a proximal algorithm for finding a common zero of a family of maximal monotone operators. In Chapter~7, the results of Chapter~6 are extended for a dynamic string-averaging version of the proximal algorithm. In Chapter~8, subgradient projection algorithms for convex feasibility problems are studied for infinite-dimensional Hilbert spaces. Theorems 2.1 and 3.1 here are known, but all other results are new. Three things, in our opinion, are important in approximating (common) fixed points: the underlying space, the iterative algorithm, and operators (or mappings) being used. The book examines different underlying spaces such as metric spaces, normed spaces, and Hilbert spaces; different algorithms such as the dynamic string-averaging method, dynamic string-maximum method, component-averaged row projections or CARP, proximal point algorithm, its generalization dynamic string-averaging proximal point method, and inexact subgradient projection algorithms; different mappings such as nonexpansive-type mappings and maximal monotone operators. Let $A$ be the underlying space, $B$ t…
reviewed by: Safeer Hussain Khan
Mathematics Subject Classification ID: 47-02
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H14
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 6856394
zbMATH Keywords: iterative algorithms
zbMATH Keywords: common fixed point problems
zbMATH Keywords: perturbations
zbMATH Keywords: dynamic string-averaging methods
zbMATH Keywords: convergence
zbMATH Keywords: component averaged row projections
zbMATH Keywords: maximal monotone operators
zbMATH Keywords: subgradient projection algorithms
zbMATH Keywords: convex feasibility problems
zbMATH Keywords: metric spaces
zbMATH Keywords: normed spaces
zbMATH Keywords: Hilbert spaces
author: Alexander J. Zaslavski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-77437-4
OpenAlex ID: W2802681976
Recommended article: Q2944025
Recommended article: Algorithms of common solutions to quasi variational inclusion and fixed point problems
Recommended article: Algorithm of Common Solutions to the Cayley Inclusion and Fixed Point Problems
Recommended article: Q4733679
Recommended article: Approximate solutions of common fixed-point problems
Recommended article: Algorithms for treating equilibrium and fixed point problems
Recommended article: Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems
Recommended article: Algorithmic and analytical approach to the split common fixed points problem
Recommended article: Asymptotic behavior of two algorithms for solving common fixed point problems
Recommended article: Hybrid algorithms for equilibrium and common fixed point problems with applications
description: scientific article; zbMATH DE number 6856394