Fixed Point Theory and Graph Theory Book

Fixed Point Theory and Graph Theory


  • Author : Monther Alfuraidan
  • Publisher : Academic Press
  • Release Date : 2016-06-20
  • Genre: Mathematics
  • Pages : 442
  • ISBN 10 : 9780128043653

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Fixed Point Theory and Graph Theory Excerpt :

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

Topological Fixed Point Theory of Multivalued Mappings Book

Topological Fixed Point Theory of Multivalued Mappings


  • Author : Lech Górniewicz
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-11
  • Genre: Mathematics
  • Pages : 403
  • ISBN 10 : 9789401591959

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Topological Fixed Point Theory of Multivalued Mappings Excerpt :

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 to the homo logical methods and contains more general results, e. g. , the Lefschetz Fixed Point Theorem, the fixed point index and the topological degree theory. In Chapter V applications to some special problems in fixed point theory are formulated. Then in the last chapter a direct application's to differential inclusions are presented. Note that Chapter I and Chapter II have an auxiliary character, and only results con nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the fixed point theory. In the last section of our book (see Section 75) we give a bibliographical guide and also signal some further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and com mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. Gorka, M. Gorniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.

Handbook of Metric Fixed Point Theory Book
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Handbook of Metric Fixed Point Theory


  • Author : W.A. Kirk
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 704
  • ISBN 10 : 9789401717489

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Handbook of Metric Fixed Point Theory Excerpt :

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 study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide 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.

Fixed Point Theory in Distance Spaces Book

Fixed Point Theory in Distance Spaces


  • Author : William Kirk
  • Publisher : Springer
  • Release Date : 2014-10-23
  • Genre: Mathematics
  • Pages : 173
  • ISBN 10 : 9783319109275

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Fixed Point Theory in Distance Spaces Excerpt :

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’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.

Topics in Metric Fixed Point Theory Book

Topics in Metric Fixed Point Theory


  • Author : Kazimierz Goebel
  • Publisher : Cambridge University Press
  • Release Date : 1990
  • Genre: Mathematics
  • Pages : 258
  • ISBN 10 : 0521382890

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Topics in Metric Fixed Point Theory Excerpt :

Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.

Metric Fixed Point Theory Book

Metric Fixed Point Theory


  • Author : Pradip Debnath
  • Publisher : Springer
  • Release Date : 2022-02-10
  • Genre: Mathematics
  • Pages : 353
  • ISBN 10 : 9811648956

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Metric Fixed Point Theory Excerpt :

This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.

Metric Fixed Point Theory Book

Metric Fixed Point Theory


  • Author : Pradip Debnath
  • Publisher : Springer Nature
  • Release Date : 2022-01-04
  • Genre: Mathematics
  • Pages : 353
  • ISBN 10 : 9789811648960

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Metric Fixed Point Theory Excerpt :

This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.

Fixed Point Theory and Related Topics Book

Fixed Point Theory and Related Topics


  • Author : Hsien-ChungWu
  • Publisher : MDPI
  • Release Date : 2020-03-13
  • Genre: Mathematics
  • Pages : 236
  • ISBN 10 : 9783039284320

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Fixed Point Theory and Related Topics Excerpt :

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 a partial metric space, b-metric space, fuzzy metric space and probabilistic metric space, etc. Different spaces will result in different types of fixed point theorems. In other words, there are a lot of different types of fixed point theorems in the literature. Therefore, this Special Issue welcomes survey articles. Articles that unify the different types of fixed point theorems are also very welcome. The topics of this Special Issue include the following: Fixed point theorems in metric space Fixed point theorems in fuzzy metric space Fixed point theorems in probabilistic metric space Fixed point theorems of set-valued functions in various spaces The existence of solutions in game theory The existence of solutions for equilibrium problems The existence of solutions of differential equations The existence of solutions of integral equations Numerical methods for obtaining the approximated fixed points

Evasiveness of Graph Properties and Topological Fixed Point Theorems Book

Evasiveness of Graph Properties and Topological Fixed Point Theorems


  • Author : Carl A. Miller
  • Publisher : Unknown
  • Release Date : 2013
  • Genre: Combinatorial analysis
  • Pages : 81
  • ISBN 10 : 1601986645

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Evasiveness of Graph Properties and Topological Fixed Point Theorems Excerpt :

Evasiveness of Graph Properties and Topological Fixed-Point Theorems provides the reader with an integrated treatment of the underlying proofs in the body of research around the use of topological methods to prove lower bounds on the complexity of graph properties.

Advances in Metric Fixed Point Theory and Applications Book

Advances in Metric Fixed Point Theory and Applications


  • Author : Yeol Je Cho
  • Publisher : Springer Nature
  • Release Date : 2021-06-05
  • Genre: Mathematics
  • Pages : 503
  • ISBN 10 : 9789813366473

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Advances in Metric Fixed Point Theory and Applications Excerpt :

This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators. This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.

Advanced Fixed Point Theory for Economics Book

Advanced Fixed Point Theory for Economics


  • Author : Andrew McLennan
  • Publisher : Springer
  • Release Date : 2018-07-03
  • Genre: Business & Economics
  • Pages : 432
  • ISBN 10 : 9789811307102

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Advanced Fixed Point Theory for Economics Excerpt :

This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.

Ordered Sets Book

Ordered Sets


  • Author : Bernd Schröder
  • Publisher : Birkhäuser
  • Release Date : 2016-05-11
  • Genre: Mathematics
  • Pages : 420
  • ISBN 10 : 9783319297880

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Ordered Sets Excerpt :

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Advanced Topics in Mathematical Analysis Book
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Advanced Topics in Mathematical Analysis


  • Author : Michael Ruzhansky
  • Publisher : CRC Press
  • Release Date : 2019-01-08
  • Genre: Mathematics
  • Pages : 588
  • ISBN 10 : 9781351142113

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Advanced Topics in Mathematical Analysis Excerpt :

Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

The Seventh European Conference on Combinatorics  Graph Theory and Applications Book

The Seventh European Conference on Combinatorics Graph Theory and Applications


  • Author : Jaroslav Nešetřil
  • Publisher : Springer Science & Business Media
  • Release Date : 2014-01-18
  • Genre: Mathematics
  • Pages : 600
  • ISBN 10 : 9788876424755

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The Seventh European Conference on Combinatorics Graph Theory and Applications Excerpt :

In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.