Measures of Noncompactness in Metric Fixed Point Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Measures of Noncompactness in Metric Fixed Point Theory PDF full book. Access full book title Measures of Noncompactness in Metric Fixed Point Theory by J.M. Ayerbe Toledano. Download full books in PDF and EPUB format.
Author: J.M. Ayerbe Toledano
Publisher: Birkhäuser
ISBN: 3034889208
Category : Mathematics
Languages : en
Pages : 222
Get Book Here
Book Description
What is clear and easy to grasp attracts us; complications deter David Hilbert The material presented in this volume is based on discussions conducted in peri odically held seminars by the Nonlinear Functional Analysis research group of the University of Seville. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see [AKPRSj, [BG]) or in books on metric fixed point theory (see [GK1], [Sm], [Z]). Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. However, as in any work of this type, an effort has been made to revise many proofs and to place many others in a correct setting. Our research was made possible by partial support of the D.G.I.C.y'T. and the Junta de Andalucia.
Author: J.M. Ayerbe Toledano
Publisher: Birkhäuser
ISBN: 3034889208
Category : Mathematics
Languages : en
Pages : 222
Get Book Here
Book Description
What is clear and easy to grasp attracts us; complications deter David Hilbert The material presented in this volume is based on discussions conducted in peri odically held seminars by the Nonlinear Functional Analysis research group of the University of Seville. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see [AKPRSj, [BG]) or in books on metric fixed point theory (see [GK1], [Sm], [Z]). Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. However, as in any work of this type, an effort has been made to revise many proofs and to place many others in a correct setting. Our research was made possible by partial support of the D.G.I.C.y'T. and the Junta de Andalucia.
Author: S. A. Mohiuddine
Publisher: CRC Press
ISBN: 1040013325
Category : Mathematics
Languages : en
Pages : 205
Get Book Here
Book Description
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.
Author: Vittorino Pata
Publisher: Springer Nature
ISBN: 3030196704
Category : Mathematics
Languages : en
Pages : 171
Get Book Here
Book Description
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: S. A. Mohiuddine
Publisher: CRC Press
ISBN: 1040013368
Category : Mathematics
Languages : en
Pages : 222
Get Book Here
Book Description
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: • Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm • Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra • Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem • Discusses best proximity point results using measure of noncompactness and its applications • Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.
Author: Ravi P. Agarwal
Publisher: Cambridge University Press
ISBN: 1139433792
Category : Mathematics
Languages : en
Pages : 182
Get Book Here
Book Description
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: Mohamed A. Khamsi
Publisher: Birkhäuser
ISBN: 3319140515
Category : Mathematics
Languages : en
Pages : 251
Get Book Here
Book Description
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: Aref Jeribi
Publisher: CRC Press
ISBN: 1498733891
Category : Mathematics
Languages : en
Pages : 369
Get Book Here
Book Description
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices w
Author: Vasile I. Istrățescu
Publisher: D Reidel Publishing Company
ISBN: 9789027712240
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
Author: W.A. Kirk
Publisher: Springer Science & Business Media
ISBN: 9401717486
Category : Mathematics
Languages : en
Pages : 702
Get Book Here
Book Description
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.
Author: Yeol Je Cho
Publisher: Springer Nature
ISBN: 9813366478
Category : Mathematics
Languages : en
Pages : 512
Get Book Here
Book Description
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.
