Fixed Point Theory For Lipschitzian Type Mappings With Applications

Author : Ravi P. Agarwal,Donal O'Regan,D. R. Sahu
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 44,5 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 : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 45,9 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 : Yeol Je Cho
Publisher : Nova Publishers
Page : 220 pages
File Size : 47,7 Mb
Release : 2002
Category : Mathematics
ISBN : 1590331893

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Fixed Point Theory and Applications by Yeol Je Cho Pdf

Fixed Point Theory & Applications Volume II

Author : Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 45,7 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9783319015866

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Topics in Fixed Point Theory by Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi Pdf

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents 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. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.

Author : W.A. Kirk,B. Sims
Publisher : Springer Science & Business Media
Page : 702 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401717489

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Handbook of Metric Fixed Point Theory by W.A. Kirk,B. Sims Pdf

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 : Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro
Publisher : Springer
Page : 385 pages
File Size : 52,5 Mb
Release : 2016-03-24
Category : Mathematics
ISBN : 9783319240824

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Fixed Point Theory in Metric Type Spaces by Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro Pdf

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.

Author : Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer Nature
Page : 503 pages
File Size : 46,9 Mb
Release : 2021-06-05
Category : Mathematics
ISBN : 9789813366473

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Advances in Metric Fixed Point Theory and Applications by Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro Pdf

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.

Author : Beata Randrianantoanina,Narcisse Randrianantoanina
Publisher : Walter de Gruyter
Page : 472 pages
File Size : 51,7 Mb
Release : 2007
Category : Mathematics
ISBN : 311019449X

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Banach Spaces and Their Applications in Analysis by Beata Randrianantoanina,Narcisse Randrianantoanina Pdf

In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.

Author : Mohamed A. Khamsi,Wojciech M. Kozlowski
Publisher : Birkhäuser
Page : 245 pages
File Size : 50,7 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 : Pradip Debnath,Nabanita Konwar,Stojan Radenović
Publisher : Springer Nature
Page : 356 pages
File Size : 41,9 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 : Afif Ben Amar,Donal O'Regan
Publisher : Springer
Page : 194 pages
File Size : 49,9 Mb
Release : 2016-05-04
Category : Mathematics
ISBN : 9783319319483

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Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications by Afif Ben Amar,Donal O'Regan Pdf

This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of axiomatic measures of weak noncompactness. The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray–Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and both bounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games. Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors.

Author : Vittorino Pata
Publisher : Springer Nature
Page : 171 pages
File Size : 52,9 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 : Kok Keong Tan
Publisher : World Scientific
Page : 394 pages
File Size : 51,6 Mb
Release : 1992-08-08
Category : Electronic
ISBN : 9789814554305

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Fixed Point Theory And Applications - Proceedings Of The Second International Conference by Kok Keong Tan Pdf

This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.

Author : Robert C. Sine
Publisher : American Mathematical Soc.
Page : 253 pages
File Size : 43,7 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821850183

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Fixed Points and Nonexpansive Mappings by Robert C. Sine Pdf

Author : Terry E. Moschandreou
Publisher : BoD – Books on Demand
Page : 184 pages
File Size : 41,6 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9781789231564

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Differential Equations by Terry E. Moschandreou Pdf

The editor has incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis. The authors of each section bring a strong emphasis on theoretical foundations to the book.