Fixed Point Theory And Its Applications

Author : Ravi P. Agarwal,Donal O'Regan,D. R. Sahu
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 53,9 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9780387758183

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Fixed Point Theory for Lipschitzian-type Mappings with Applications by Ravi P. Agarwal,Donal O'Regan,D. R. Sahu Pdf

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields. This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Author : Anita Tomar,Mohan C. Joshi
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 2021
Category : Fixed point theory
ISBN : 1536193364

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Fixed Point Theory and Its Applications to Real World Problems by Anita Tomar,Mohan C. Joshi Pdf

"Fixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping. The book "Fixed Point Theory & its Applications to Real World Problems" is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library"--

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 50,6 Mb
Release : 2001-03-22
Category : Mathematics
ISBN : 9781139433792

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Fixed Point Theory and Applications by Ravi P. Agarwal,Maria Meehan,Donal O'Regan Pdf

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.

Author : Vittorino Pata
Publisher : Springer Nature
Page : 171 pages
File Size : 47,5 Mb
Release : 2019-09-22
Category : Mathematics
ISBN : 9783030196707

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Fixed Point Theorems and Applications by Vittorino Pata Pdf

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, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.

Author : Siegfried Carl,Seppo Heikkilä
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 51,5 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441975850

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Fixed Point Theory in Ordered Sets and Applications by Siegfried Carl,Seppo Heikkilä Pdf

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Author : Pradip Debnath,Nabanita Konwar,Stojan Radenović
Publisher : Springer Nature
Page : 356 pages
File Size : 41,5 Mb
Release : 2022-01-04
Category : Mathematics
ISBN : 9789811648960

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Metric Fixed Point Theory by Pradip Debnath,Nabanita Konwar,Stojan Radenović Pdf

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.

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 51,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401591959

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Topological Fixed Point Theory of Multivalued Mappings by Lech Górniewicz Pdf

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.

Author : O. Hadzic,E. Pap
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 53,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401715607

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Fixed Point Theory in Probabilistic Metric Spaces by O. Hadzic,E. Pap Pdf

Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.

Author : Kim C. Border
Publisher : Cambridge University Press
Page : 144 pages
File Size : 48,9 Mb
Release : 1985
Category : Business & Economics
ISBN : 0521388082

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Fixed Point Theorems with Applications to Economics and Game Theory by Kim C. Border Pdf

This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.

Author : Erdal Karapinar,Juan Mart ́ınez-Moreno,Inci M Erhan
Publisher : Mdpi AG
Page : 220 pages
File Size : 55,6 Mb
Release : 2021-09-30
Category : Mathematics
ISBN : 3036520716

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Theory and Application of Fixed Point by Erdal Karapinar,Juan Mart ́ınez-Moreno,Inci M Erhan Pdf

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.

Author : Ioannis Farmakis,Martin A. Moskowitz
Publisher : World Scientific
Page : 247 pages
File Size : 42,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814458924

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Fixed Point Theorems and Their Applications by Ioannis Farmakis,Martin A. Moskowitz Pdf

This is the only book that deals comprehensively with fixed point theorems overall of mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers.

Author : Mohamed A. Khamsi,Wojciech M. Kozlowski
Publisher : Birkhäuser
Page : 251 pages
File Size : 53,9 Mb
Release : 2015-03-24
Category : Mathematics
ISBN : 9783319140513

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Fixed Point Theory in Modular Function Spaces by Mohamed A. Khamsi,Wojciech M. Kozlowski Pdf

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. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.​

Author : Vasile I. Istrățescu
Publisher : D Reidel Publishing Company
Page : 0 pages
File Size : 49,8 Mb
Release : 1981
Category : Mathematics
ISBN : 9027712247

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Fixed Point Theory by Vasile I. Istrățescu Pdf

Author : Andrzej Fryszkowski
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 42,5 Mb
Release : 2006-02-21
Category : Mathematics
ISBN : 9781402024993

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Fixed Point Theory for Decomposable Sets by Andrzej Fryszkowski Pdf

Decomposable sets since T. R. Rockafellar in 1968 are one of basic notions in nonlinear analysis, especially in the theory of multifunctions. A subset K of measurable functions is called decomposable if (Q) for all and measurable A. This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property. Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.

Author : Andrzej Granas,James Dugundji
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387215938

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Fixed Point Theory by Andrzej Granas,James Dugundji Pdf

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS