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The Krasnoselskii Mann Method For Common Fixed Point Problems

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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.

The Krasnoselskii Mann Method For Common Fixed Point Problems

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Author : Aleksandr J. Zaslavskij
language : en
Publisher:
Release Date : 2025

The Krasnoselskii Mann Method For Common Fixed Point Problems written by Aleksandr J. Zaslavskij and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Mathematical optimization categories.

Approximate Fixed Points Of Nonexpansive Mappings

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2024-09-25

Approximate Fixed Points Of Nonexpansive Mappings 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 2024-09-25 with Mathematics categories.

Fixed point theory of nonlinear operators has been a rapidly growing area of research and plays an important role in the study of variational inequalities, monotone operators, feasibility problems, and optimization theory, to name just several. This book discusses iteration processes associated with a given nonlinear mapping which generate its approximate fixed point and in some cases converge to a fixed point of the mapping. Various classes of nonlinear single-valued and set-valued mappings are considered along with iteration processes under the presence of computational errors. Of particular interest to mathematicians working in fixed point theory and nonlinear analysis, the added value for the reader are the solutions presented to a number of difficult problems in the fixed point theory which have important applications.

Fixed Point Algorithms For Inverse Problems In Science And Engineering

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Author : Heinz H. Bauschke
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27

Fixed Point Algorithms For Inverse Problems In Science And Engineering written by Heinz H. Bauschke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Mathematics categories.

"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

Fixed Points Of Nonlinear Operators

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Author : Haiyun Zhou
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-06-08

Fixed Points Of Nonlinear Operators written by Haiyun Zhou and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-08 with Mathematics categories.

Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.

Topics In Fixed Point Theory

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Author : Saleh Almezel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-23

Topics In Fixed Point Theory written by Saleh Almezel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Mathematics categories.

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.

Iaeng Transactions On Engineering Sciences Special Issue For The International Association Of Engineers Conferences 2014

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Author : Sio-iong Ao
language : en
Publisher: World Scientific
Release Date : 2015-03-11

Iaeng Transactions On Engineering Sciences Special Issue For The International Association Of Engineers Conferences 2014 written by Sio-iong Ao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-11 with Technology & Engineering categories.

Two large international conferences on Advances in Engineering Sciences were held in Hong Kong, March 12-14, 2014, under the International MultiConference of Engineers and Computer Scientists (IMECS 2014), and in London, UK, 2-4 July, 2014, under the World Congress on Engineering 2014 (WCE 2014) respectively. This volume contains 37 revised and extended research articles written by prominent researchers participating in the conferences. Topics covered include engineering mathematics, computer science, electrical engineering, manufacturing engineering, industrial engineering, and industrial applications. The book offers tremendous state-of-the-art advances in engineering sciences and also serves as an excellent reference work for researchers and graduate students working with/on engineering sciences.

Fixed Point Theory And Graph Theory

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Author : Monther Alfuraidan
language : en
Publisher: Academic Press
Release Date : 2016-06-20

Fixed Point Theory And Graph Theory written by Monther Alfuraidan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.

Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. - Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments - Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach - Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications

Geometric Properties Of Banach Spaces And Nonlinear Iterations

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Author : Charles Chidume
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-27

Geometric Properties Of Banach Spaces And Nonlinear Iterations written by Charles Chidume and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-27 with Mathematics categories.

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Linear Functional Analysis

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Author : Hans Wilhelm Alt
language : en
Publisher: Springer
Release Date : 2016-07-06

Linear Functional Analysis written by Hans Wilhelm Alt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-06 with Mathematics categories.

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

The Krasnoselskii Mann Method For Common Fixed Point Problems

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