Elementary Fixed Point Theorems

Author : P. V. Subrahmanyam
Publisher : Unknown
Page : 302 pages
File Size : 46,7 Mb
Release : 2018
Category : Global analysis (Mathematics)
ISBN : 9811331596

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Elementary Fixed Point Theorems by P. V. Subrahmanyam Pdf

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky's theorem on periodic points, Thron's results on the convergence of certain real iterates, Shield's common fixed theorem for a commuting family of analytic functions and Bergweiler's existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski's theorem by Merrifield and Stein and Abian's proof of the equivalence of Bourbaki-Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward's theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka's proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy-Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder-Gohde-Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.

Author : P.V. Subrahmanyam
Publisher : Springer
Page : 302 pages
File Size : 52,9 Mb
Release : 2019-01-10
Category : Mathematics
ISBN : 9789811331589

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Elementary Fixed Point Theorems by P.V. Subrahmanyam Pdf

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky’s theorem on periodic points, Thron’s results on the convergence of certain real iterates, Shield’s common fixed theorem for a commuting family of analytic functions and Bergweiler’s existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski’s theorem by Merrifield and Stein and Abian’s proof of the equivalence of Bourbaki–Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward’s theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka’s proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy–Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder–Gohde–Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.

Author : Andrzej Granas,James Dugundji
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 54,9 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

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 42,8 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 : D. R. Smart
Publisher : CUP Archive
Page : 108 pages
File Size : 50,7 Mb
Release : 1980-02-14
Category : Mathematics
ISBN : 0521298334

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Fixed Point Theorems by D. R. Smart Pdf

Author : Vittorino Pata
Publisher : Springer Nature
Page : 171 pages
File Size : 43,9 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 : Ioannis Farmakis,Martin Moskowitz
Publisher : World Scientific
Page : 248 pages
File Size : 45,8 Mb
Release : 2013-07-26
Category : Mathematics
ISBN : 9789814458931

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

This is the only book that deals comprehensively with fixed point theorems throughout 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. Contents:Early Fixed Point TheoremsFixed Point Theorems in AnalysisThe Lefschetz Fixed Point TheoremFixed Point Theorems in GeometryFixed Points of Volume Preserving MapsBorel's Fixed Point Theorem in Algebraic GroupsMiscellaneous Fixed Point TheoremsA Fixed Point Theorem in Set Theory Readership: Graduate students and professionals in analysis, approximation theory, algebra and geometry. Keywords:Fixed Point Theorems in Analysis;Topology;Geometry;Dynamical Systems;Algebraic Groups;Set TheoryKey Features:Our book gives a complete treatment of the diverse and manifold use of fixed point theorems and their many applications throughout Mathematics and is another example of the unity within MathematicsAs such it serves as a valuable resource for researchers in diverse fields of MathematicsIt also serves as solid introduction for students to several subjects in modern Mathematics such as Functional Analysis, Topology, Differential Geometry, Dynamical Systems and Algebraic GroupsReviews: “The book presents interest mainly by some more special fixed point theorems in algebraic topology, algebraic geometry, and differential and symplectic geometry, as well as by the interesting applications of fixed point results to various areas of mathematics. Written in a way that the chapters can be used independently it appeals to a large audience.” Adrian Petrusel Stud. Univ. Babes-Bolyai Math “This book provides a rich source of information on fixed point theorems in various branches of mathematics.” Zentralblatt MATH “This is an enjoyable book about various aspects of fixed point theory. It presents a pleasurable journey through various areas of modern mathematics, guided by two experts with a predilection for fixed point theory. Reading this book will be great fun for the educated mathematician.” Mathematical Reviews Clippings

Author : Rajinder Sharma
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2021
Category : Fixed point theory
ISBN : 1536195650

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An In-Depth Guide to Fixed-Point Theorems by Rajinder Sharma Pdf

"This book details fixed point theory, a gripping and wide-ranging field with applications in multifold areas of pure and applied mathematics. The content comprises both theoretical and practical applications. The evolution of the main theorems on the existence and uniqueness of fixed points of maps are presented. Applications covering topological properties, a nonlinear stochastic integral equation of the Hammerstein type, the existence and uniqueness of a common solution of the system of Urysohn integral equations, and the existence of a unique solution for linear equations system are included in this selection. Since the included chapters range from broad elucidations to functional research papers, the book provides readers with a satisfying analysis of the subject as well as a more comprehensive look at some functional recent advances"--

Author : Qamrul Hasan Ansari,Daya Ram Sahu
Publisher : Cambridge University Press
Page : 236 pages
File Size : 53,6 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781009392747

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Fixed Point Theory and Variational Principles in Metric Spaces by Qamrul Hasan Ansari,Daya Ram Sahu Pdf

The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. Basic techniques and results of topics such as fixed point theory, set-valued analysis, variational principles, and equilibrium problems are presented in an understandable and thorough manner.

Author : Hemant Kumar Pathak
Publisher : Springer
Page : 830 pages
File Size : 47,6 Mb
Release : 2018-05-19
Category : Mathematics
ISBN : 9789811088667

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An Introduction to Nonlinear Analysis and Fixed Point Theory by Hemant Kumar Pathak Pdf

This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.

Author : Praveen Agarwal,Mohamed Jleli,Bessem Samet
Publisher : Springer
Page : 166 pages
File Size : 48,8 Mb
Release : 2018-12-18
Category : Mathematics
ISBN : 9811329125

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Fixed Point Theory in Metric Spaces by Praveen Agarwal,Mohamed Jleli,Bessem Samet Pdf

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials. The book is a valuable resource for a wide audience, including graduate students and researchers.

Author : Kazimierz Goebel,W. A. Kirk
Publisher : Cambridge University Press
Page : 258 pages
File Size : 52,6 Mb
Release : 1990
Category : Mathematics
ISBN : 0521382890

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Topics in Metric Fixed Point Theory by Kazimierz Goebel,W. A. Kirk Pdf

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.

Author : Schaefer, Uwe
Publisher : KIT Scientific Publishing
Page : 150 pages
File Size : 53,8 Mb
Release : 2014-12-03
Category : Mathematics
ISBN : 9783731502609

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From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications by Schaefer, Uwe Pdf

Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.

Author : Joel H. Shapiro
Publisher : Springer
Page : 221 pages
File Size : 53,6 Mb
Release : 2016-05-23
Category : Mathematics
ISBN : 9783319279787

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A Fixed-Point Farrago by Joel H. Shapiro Pdf

This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll–Nardzewski surrounding fixed points for families of affine maps.

Author : Uwe Schäfer
Publisher : Unknown
Page : 146 pages
File Size : 51,7 Mb
Release : 2020-10-09
Category : Mathematics
ISBN : 1013280741

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From Sperner's Lemma to Differential Equations in Banach Spaces by Uwe Schäfer Pdf

Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.