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Fixed Point Theory and Graph Theory

Fixed Point Theory and Graph Theory
Foundations and Integrative Approaches

by Monther Alfuraidan,Qamrul Ansari

  • Publisher : Academic Press
  • Release : 2016-06-20
  • Pages : 442
  • ISBN : 0128043652
  • Language : En, Es, Fr & De
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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

Topological Fixed Point Theory of Multivalued Mappings
A Book

by Lech Górniewicz

  • Publisher : Springer Science & Business Media
  • Release : 2006-06-03
  • Pages : 538
  • ISBN : 1402046669
  • Language : En, Es, Fr & De
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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.

Fixed Point Theory and Applications

Fixed Point Theory and Applications
A Book

by Ravi P. Agarwal,Maria Meehan,Donal O'Regan

  • Publisher : Cambridge University Press
  • Release : 2001-03-22
  • Pages : 170
  • ISBN : 9781139433792
  • Language : En, Es, Fr & De
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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 and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Handbook of Metric Fixed Point Theory

Handbook of Metric Fixed Point Theory
A Book

by William Kirk,Brailey Sims

  • Publisher : Springer Science & Business Media
  • Release : 2001-06-30
  • Pages : 703
  • ISBN : 9780792370734
  • Language : En, Es, Fr & De
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Preface. 1. Contraction Mappings and Extensions; W.A. Kirk. 2. Examples of Fixed Point Free Mappings; B. Sims. 3. Classical Theory of Nonexpansive Mappings; K. Goebel, W.A. Kirk. 4. Geometrical Background of Metric Fixed Point Theory; S. Prus. 5. Some Moduli and Constants Related to Metric Fixed Point Theory; E.L. Fuster. 6. Ultra-Methods in Metric Fixed Point Theory; M.A. Khamsi, B. Sims. 7. Stability of the Fixed Point Property for Nonexpansive Mappings; J. Garcia-Falset, A. Jiménez-Melado, E. Llorens-Fuster. 8. Metric Fixed Point Results Concerning Measures of Noncompactness; T. Dominguez, M.A. JapÃ3n, G. LÃ3pez. 9. Renormings of l1 and c0 and Fixed Point Properties; P.N. Dowling, C.J. Lennard, B. Turett. 10. Nonexpansive Mappings: Boundary/Inwardness Conditions and Local Theory; W.A. Kirk, C.H. Morales. 11. Rotative Mappings and Mappings with Constant Displacement; W. Kaczor, M. Koter-MÃ3rgowska. 12. Geometric Properties Related to Fixed Point Theory in Some Banach Function Lattices; S. Chen, Y. Cui, H. Hudzik, B. Sims. 13. Introduction to Hyperconvex Spaces; R. Espinola, M.A. Khamsi. 14. Fixed Points of Holomorphic Mappings: A Metric Approach; T. Kuczumow, S. Reich, D. Shoikhet. 15. Fixed Point and Non-Linear Ergodic Theorems for Semigroups of Non-Linear Mappings; A. To-Ming Lau, W. Takahashi. 16. Generic Aspects of Metric Fixed Point Theory; S. Reich, A.J. Zaslavski. 17. Metric Environment of the Topological Fixed Point Theorms; K. Goebel. 18. Order-Theoretic Aspects of Metric Fixed Point Theory; J. Jachymski. 19. Fixed Point and Related Theorems for Set-Valued Mappings; G.X.-Z. Yuan. Index.

Fixed Point Theorems with Applications to Economics and Game Theory

Fixed Point Theorems with Applications to Economics and Game Theory
A Book

by Kim C. Border

  • Publisher : Cambridge University Press
  • Release : 1985
  • Pages : 129
  • ISBN : 9780521388085
  • Language : En, Es, Fr & De
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This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.

Fixed Point Theory in Distance Spaces

Fixed Point Theory in Distance Spaces
A Book

by William Kirk,Naseer Shahzad

  • Publisher : Springer
  • Release : 2014-10-23
  • Pages : 173
  • ISBN : 3319109278
  • Language : En, Es, Fr & De
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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.

Fixed Point Theory and Related Topics

Fixed Point Theory and Related Topics
A Book

by Hsien-ChungWu

  • Publisher : MDPI
  • Release : 2020-03-13
  • Pages : 236
  • ISBN : 3039284320
  • Language : En, Es, Fr & De
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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

Higher-Order Fixed Point Theory in Partial Metric Spaces: Some Results Generalizing the Hardy-Rogers Map

Higher-Order Fixed Point Theory in Partial Metric Spaces: Some Results Generalizing the Hardy-Rogers Map
A Book

by Clement Ampadu

  • Publisher : Lulu.com
  • Release : 2021
  • Pages : 329
  • ISBN : 136556360X
  • Language : En, Es, Fr & De
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Fixed Point Theory

Fixed Point Theory
An Introduction

by V.I. Istratescu

  • Publisher : Springer
  • Release : 2001-11-30
  • Pages : 488
  • ISBN : 9781402003011
  • Language : En, Es, Fr & De
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Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will find the final G. K. Chesterton, The Scandal of Father question. Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

The Role of Various Kinds of Continuity in the Fixed Point Theory of Set-valued Mappings

The Role of Various Kinds of Continuity in the Fixed Point Theory of Set-valued Mappings
A Book

by Dariusz Miklaszewski,Mieczyslaw K. Mentzen

  • Publisher : Unknown Publisher
  • Release : 2005
  • Pages : 73
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Topological Graph Theory

Topological Graph Theory
A Book

by Jonathan L. Gross,Jonathan L.. Gross,Thomas W. Tucker,Brad G. Osgood

  • Publisher : Wiley-Interscience
  • Release : 1987-07-13
  • Pages : 351
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This definitive treatment written by well-known experts emphasizes graph imbedding while providing thorough coverage of the connections between topological graph theory and other areas of mathematics: spaces, finite groups, combinatorial algorithms, graphical enumeration, and block design. Almost every result of studies in this field is covered, including most proofs and methods. Its numerous examples and clear presentation simplify conceptually difficult material, making the text accessible to students as well as researchers. Includes an extensive list of references to current literature.

Seminar on Fixed Point Theory

Seminar on Fixed Point Theory
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1983
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Graph Theory with Applications

Graph Theory with Applications
A Book

by John Adrian Bondy,U. S. R. Murty

  • Publisher : London : Macmillan Press
  • Release : 1976
  • Pages : 264
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Mathematical Reviews

Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Graph Theory Bibliography with Two Level Key-word Index: Key-word index. Author index

Graph Theory Bibliography with Two Level Key-word Index: Key-word index. Author index
A Book

by Gerald Berman

  • Publisher : Unknown Publisher
  • Release : 1983
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Proceedings of the Southeastern Conference on Combinatorics, Graph Theory, and Computing

Proceedings of the Southeastern Conference on Combinatorics, Graph Theory, and Computing
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1992
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Topological Fixed Point Theory and Applications

Topological Fixed Point Theory and Applications
Proceedings of a Conference Held at the Nankai Institute of Mathematics, Tianjin, PR China, April 5-8, 1988

by Boju Jiang

  • Publisher : Springer Verlag
  • Release : 1989-11-28
  • Pages : 203
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.

Index of Mathematical Papers

Index of Mathematical Papers
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1974
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Lectures on Nielsen Fixed Point Theory

Lectures on Nielsen Fixed Point Theory
A Book

by Boju Jiang

  • Publisher : Amer Mathematical Society
  • Release : 1983
  • Pages : 110
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Starting with the simplest examples, this book gives an easy introduction to the subject, then explains several very recent developments. It makes available in the English language the covering space approach to Nielsen fixed point theory. As far as research value is concerned, the Nielsen theory of periodic points is published here for the first time, and an exposition and improvement of the latest progress in the Nielsen theory of fiber maps is provided.

Homological Methods in Fixed-point Theory of Multi-valued Maps

Homological Methods in Fixed-point Theory of Multi-valued Maps
A Book

by Lech Górniewicz

  • Publisher : Unknown Publisher
  • Release : 1976
  • Pages : 71
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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