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The Krasnoselskii-Mann method for common fixed point problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Krasnoselskii-Mann method for common fixed point problems/ by Alexander J. Zaslavski.
Author:	Zaslavski, Alexander J.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	viii, 137 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Iterative methods -- Methods with remotest set control -- Set-valued inclusions -- The Cimmino algorithm in a normed space -- Dynamic string-averaging methods -- References.
Contained By:	Springer Nature eBook
Subject:	Fixed point theory. -
Online resource:	https://doi.org/10.1007/978-3-031-85841-3
ISBN:	9783031858413

The Krasnoselskii-Mann method for common fixed point problems
Zaslavski, Alexander J.

The Krasnoselskii-Mann method for common fixed point problems[electronic resource] /by Alexander J. Zaslavski. - Cham :Springer Nature Switzerland :2025. - viii, 137 p. :ill., digital ;24 cm. - SpringerBriefs in optimization,2191-575X. - SpringerBriefs in optimization..

Introduction -- Iterative methods -- Methods with remotest set control -- Set-valued inclusions -- The Cimmino algorithm in a normed space -- Dynamic string-averaging methods -- References.

This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces. Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.

ISBN: 9783031858413

Standard No.: 10.1007/978-3-031-85841-3doiSubjects--Topical Terms:

546826
Fixed point theory.

LC Class. No.: QA329.9

Dewey Class. No.: 515.7248

The Krasnoselskii-Mann method for common fixed point problems
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490 1 $a SpringerBriefs in optimization, $x 2191-575X
505 0 $a Introduction -- Iterative methods -- Methods with remotest set control -- Set-valued inclusions -- The Cimmino algorithm in a normed space -- Dynamic string-averaging methods -- References.
520 $a This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces. Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.
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