Fixed Point Theory and Graph Theory

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

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  • Author : Monther Alfuraidan
  • Publisher : Academic Press
  • Pages : 442 pages
  • ISBN : 0128043652
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKFixed Point Theory and Graph Theory

Fixed Point Theory and Graph Theory

Fixed Point Theory and Graph Theory
  • Author : Monther Alfuraidan,Qamrul Ansari
  • Publisher : Academic Press
  • Release : 20 June 2016
GET THIS BOOKFixed Point Theory and Graph Theory

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

Fixed Point Theory and Applications

Fixed Point Theory and Applications
  • Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
  • Publisher : Cambridge University Press
  • Release : 22 March 2001
GET THIS BOOKFixed Point Theory and Applications

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers

Fixed Point Theory and Related Topics

Fixed Point Theory and Related Topics
  • Author : Hsien-ChungWu
  • Publisher : MDPI
  • Release : 13 March 2020
GET THIS BOOKFixed Point Theory and Related Topics

Fixed point theory arose from the Banach contraction principle and has been studied for a long time. Its application mostly relies on the existence of solutions to mathematical problems that are formulated from economics and engineering. After the existence of the solutions is guaranteed, the numerical methodology will be established to obtain the approximated solution. Fixed points of function depend heavily on the considered spaces that are defined using the intuitive axioms. In particular, variant metrics spaces are proposed, like

Topological Fixed Point Theory of Multivalued Mappings

Topological Fixed Point Theory of Multivalued Mappings
  • Author : Lech Górniewicz
  • Publisher : Springer Science & Business Media
  • Release : 11 November 2013
GET THIS BOOKTopological Fixed Point Theory of Multivalued Mappings

This book is an attempt to give a systematic presentation of results and meth ods which concern the fixed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to study ing topological methods in the fixed point theory of multivalued mappings and applications, mainly to differential inclusions. Thus in Chapter III the approximation (on the graph) method in fixed point theory of multi valued mappings is presented. Chapter IV is devoted

Topological Fixed Point Theory of Multivalued Mappings

Topological Fixed Point Theory of Multivalued Mappings
  • Author : Lech Górniewicz
  • Publisher : Springer Science & Business Media
  • Release : 03 June 2006
GET THIS BOOKTopological Fixed Point Theory of Multivalued Mappings

This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.

The Computation of Fixed Points and Applications

The Computation of Fixed Points and Applications
  • Author : M. J. Todd
  • Publisher : Springer Science & Business Media
  • Release : 09 March 2013
GET THIS BOOKThe Computation of Fixed Points and Applications

Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been

Iterative Approximation of Fixed Points

Iterative Approximation of Fixed Points
  • Author : Vasile Berinde
  • Publisher : Springer
  • Release : 20 April 2007
GET THIS BOOKIterative Approximation of Fixed Points

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Fixed Point Theory in Distance Spaces

Fixed Point Theory in Distance Spaces
  • Author : William Kirk,Naseer Shahzad
  • Publisher : Springer
  • Release : 23 October 2014
GET THIS BOOKFixed Point Theory in Distance Spaces

This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’

Fixed Point Theorems and Applications

Fixed Point Theorems and Applications
  • Author : Vittorino Pata
  • Publisher : Springer Nature
  • Release : 20 August 2019
GET THIS BOOKFixed Point Theorems and Applications

This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory,

Handbook of Metric Fixed Point Theory

Handbook of Metric Fixed Point Theory
  • Author : W.A. Kirk,B. Sims
  • Publisher : Springer Science & Business Media
  • Release : 17 April 2013
GET THIS BOOKHandbook of Metric Fixed Point Theory

Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the

Graphs & Digraphs, Fourth Edition

Graphs & Digraphs, Fourth Edition
  • Author : Gary Chartrand,Linda Lesniak,Ping Zhang
  • Publisher : CRC Press
  • Release : 28 October 2004
GET THIS BOOKGraphs & Digraphs, Fourth Edition

With a growing range of applications in fields from computer science to chemistry and communications networks, graph theory has enjoyed a rapid increase of interest and widespread recognition as an important area of mathematics. Through more than 20 years of publication, Graphs & Digraphs has remained a popular point of entry to the field, and through its various editions, has evolved with the field from a purely mathematical treatment to one that also addresses the mathematical needs of computer scientists. Carefully updated,

Fixed Point Theory in Modular Function Spaces

Fixed Point Theory in Modular Function Spaces
  • Author : Mohamed A. Khamsi,Wojciech M. Kozlowski
  • Publisher : Birkhäuser
  • Release : 24 March 2015
GET THIS BOOKFixed Point Theory in Modular Function Spaces

This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts.

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Fixed-Point Algorithms for Inverse Problems in Science and Engineering
  • Author : Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
  • Publisher : Springer Science & Business Media
  • Release : 27 May 2011
GET THIS BOOKFixed-Point Algorithms for Inverse Problems in Science and Engineering

"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,