The Krasnosel Ski Mann Iterative Method

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The Krasnosel Ski Mann Iterative Method

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Author : Qiao-Li Dong
language : en
Publisher: Springer Nature
Release Date : 2022-02-24

The Krasnosel Ski Mann Iterative Method written by Qiao-Li Dong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-24 with Mathematics categories.

This brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

The Krasnosel Ski Mann Iterative Method

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Author : Qiao-Li Dong
language : en
Publisher:
Release Date : 2022

The Krasnosel Ski Mann Iterative Method written by Qiao-Li Dong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

This brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods. .

Iterative Methods For Fixed Point Problems In Hilbert Spaces

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Author : Andrzej Cegielski
language : en
Publisher: Springer
Release Date : 2012-09-14

Iterative Methods For Fixed Point Problems In Hilbert Spaces written by Andrzej Cegielski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

The Krasnoselskii Mann Method For Common Fixed Point Problems

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2025-03-24

The Krasnoselskii Mann Method For Common Fixed Point Problems written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-24 with Mathematics categories.

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.

Differential Geometry Algebra And Analysis

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Author : Mohammad Hasan Shahid
language : en
Publisher: Springer Nature
Release Date : 2020-09-04

Differential Geometry Algebra And Analysis written by Mohammad Hasan Shahid and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-04 with Mathematics categories.

This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15–17 November 2016. It covers a wide range of topics—geometry of submanifolds, geometry of statistical submanifolds, ring theory, module theory, optimization theory, and approximation theory—which exhibit new ideas and methodologies for current research in differential geometry, algebra and analysis. Providing new results with rigorous proofs, this book is, therefore, of much interest to readers who wish to learn new techniques in these areas of mathematics.

Fixed Point Theory In P Vector Spaces

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Author : George Xianzhi Yuan
language : en
Publisher: World Scientific
Release Date : 2025-05-05

Fixed Point Theory In P Vector Spaces written by George Xianzhi Yuan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.

This monograph provides an updated development of fixed point theory under a unified framework of the 'best approximation approach' in p-vector spaces, a core component of nonlinear analysis in mathematics, where p∊(0,1] (the same for p below unless specified). This book exposes some important contents of the new fixed point theory, with highlights in four parts.Specifically, the book focuses on the development of general new fixed point theory for both single-valued and set-valued mappings under the framework of p-vector and locally convex spaces for p∊(0,1], including topological vector spaces and locally convex spaces as special cases. It provides affirmative answers to the Schauder conjecture under the general setting of p-vector spaces and locally p-convex spaces. The book establishes best approximation results for upper semicontinuous and 1-set contractive set-valued mappings, which are used as tools to establish new fixed point theorems for non-self set-valued mappings with either inward or outward set conditions under various situations. These results improve or unify corresponding results in the existing literature for nonlinear analysis and lay the foundation for the development of fixed point theorems in topological vector spaces since Schauder's conjecture was raised in 1930. In addition, this book demonstrates the power of the fixed point theorem by showing the equivalence among the Ekeland variational principle, Takahashi minimization theorem, Oettli-Théra theorem, Caristi-Kirk type fixed point theorem, and related principles in nonlinear functional analysis.Overall, this book provides an accessible way to establish the new theory in the development of fixed point theorems and results. It is designed to be understandable for senior undergraduate students majoring in mathematics, physical sciences, social sciences, and related fields. We expect that this monograph will serve as a staple textbook for undergraduate and postgraduate students, a reference book for researchers in the field of fixed point theory in nonlinear functional analysis, and an accessible resource for general readers in mathematics and related disciplines.

Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space

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Author : W.M., III. Patterson
language : en
Publisher: Springer
Release Date : 2006-11-15

Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space written by W.M., III. Patterson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.

Canadian Mathematical Bulletin

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Author :
language : en
Publisher:
Release Date : 1992-03

Canadian Mathematical Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03 with categories.

Nonlinear Analysis And Optimization I

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Author : Simeon Reich
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Nonlinear Analysis And Optimization I written by Simeon Reich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This volume is the first of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in these important fields of mathematics. This volume contains articles on nonlinear analysis. Topics covered include the convex feasibility problem, fixed point theory, mathematical biology, Mosco stability, nonexpansive mapping theory, nonlinear partial differential equations, optimal control, the proximal point algorithm and semigroup theory. The companion volume (Contemporary Mathematics, Volume 514) is devoted to optimization. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: A. S. Ackleh, K. Deng, and Q. Huang -- Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model; S. Aizicovici, N. S. Papageorgiou, and V. Staicu -- Three nontrivial solutions for $p$-Laplacian Neumann problems with a concave nonlinearity near the origin; V. Barbu -- Optimal stabilizable feedback controller for Navier-Stokes equations; H. H. Bauschke and X. Wang -- Firmly nonexpansive and Kirszbraun-Valentine extensions: A constructive approach via monotone operator theory; R. E. Bruck -- On the random product of orthogonal projections in Hilbert space II; D. Butnariu, E. Resmerita, and S. Sabach -- A Mosco stability theorem for the generalized proximal mapping; A. Cegielski -- Generalized relaxations of nonexpansive operators and convex feasibility problems; Y. Censor and A. Segal -- Sparse string-averaging and split common fixed points; T. Dominguez Benavides and S. Phothi -- Genericity of the fixed point property for reflexive spaces under renormings; K. Goebel and B. Sims -- Mean Lipschitzian mappings; T. Ibaraki and W. Takahashi -- Generalized nonexpansive mappings and a proximal-type algorithm in Banach spaces; W. Kaczor, T. Kuczumow, and N. Michalska -- The common fixed point set of commuting nonexpansive mapping in Cartesian products of weakly compact convex sets; L. Leu'tean -- Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces; G. Lopez, V. Martin-Marquez, and H.-K. Xu -- Halpern's iteration for nonexpansive mappings; J. W. Neuberger -- Lie generators for local semigroups; H.-K. Xu -- An alternative regularization method for nonexpansive mappings with applications. (CONM/513)

Solutions Of Fixed Point Problems With Computational Errors

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2024-03-19

Solutions Of Fixed Point Problems With Computational Errors written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-19 with Mathematics categories.

The book is devoted to the study of approximate solutions of fixed point problems in the presence of computational errors. It begins with a study of approximate solutions of star-shaped feasibility problems in the presence of perturbations. The goal is to show the convergence of algorithms, which are known as important tools for solving convex feasibility problems and common fixed point problems.The text also presents studies of algorithms based on unions of nonexpansive maps, inconsistent convex feasibility problems, and split common fixed point problems. A number of algorithms are considered for solving convex feasibility problems and common fixed point problems. The book will be of interest for researchers and engineers working in optimization, numerical analysis, and fixed point theory. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of the influence of computational errorsfor several important algorithms used for nonconvex feasibility problems.