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| Author | : William Kirk |
| Publisher | : Springer |
| Total Pages | : 173 |
| Release | : 2014-10-23 |
| Genre | : Mathematics |
| ISBN | : 3319109278 |
Download Fixed Point Theory in Distance Spaces Book in PDF, ePub and Kindle
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.
| Author | : Vladimir Rakočević |
| Publisher | : |
| Total Pages | : 177 |
| Release | : 2022 |
| Genre | : Fixed point theory |
| ISBN | : 9781032100586 |
Download Fixed Point Results in W-distance Spaces Book in PDF, ePub and Kindle
| Author | : Praveen Agarwal |
| Publisher | : Springer |
| Total Pages | : 166 |
| Release | : 2018-10-13 |
| Genre | : Mathematics |
| ISBN | : 9811329133 |
Download Fixed Point Theory in Metric Spaces Book in PDF, ePub and Kindle
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 | : Yeol Je Cho |
| Publisher | : Nova Publishers |
| Total Pages | : 220 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9781590331897 |
Download Fixed Point Theory and Applications Book in PDF, ePub and Kindle
Fixed Point Theory & Applications Volume II
| Author | : Ravi P. Agarwal |
| Publisher | : Springer |
| Total Pages | : 395 |
| Release | : 2016-03-24 |
| Genre | : Mathematics |
| ISBN | : 331924082X |
Download Fixed Point Theory in Metric Type Spaces Book in PDF, ePub and Kindle
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 | : Ravi P. Agarwal |
| Publisher | : Cambridge University Press |
| Total Pages | : 182 |
| Release | : 2001-03-22 |
| Genre | : Mathematics |
| ISBN | : 1139433792 |
Download Fixed Point Theory and Applications Book in PDF, ePub and Kindle
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 | : Dhananjay Gopal |
| Publisher | : CRC Press |
| Total Pages | : 317 |
| Release | : 2021-04-08 |
| Genre | : Mathematics |
| ISBN | : 1000366391 |
Download Metric Structures and Fixed Point Theory Book in PDF, ePub and Kindle
It is an indisputable argument that the formulation of metrics (by Fréchet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach’s fixed point theorem. Because the underlying space of this theorem is a metric space, the theory that developed following its publication is known as metric fixed point theory. It is well known that metric fixed point theory provides essential tools for solving problems arising in various branches of mathematics and other sciences such as split feasibility problems, variational inequality problems, non-linear optimization problems, equilibrium problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations are closely related to fixed point theory. For this reason, many people over the past seventy years have tried to generalize the definition of metric space and corresponding fixed point theory. This trend still continues. A few questions lying at the heart of the theory remain open and there are many unanswered questions regarding the limits to which the theory may be extended. Metric Structures and Fixed Point Theory provides an extensive understanding and the latest updates on the subject. The book not only shows diversified aspects of popular generalizations of metric spaces such as symmetric, b-metric, w-distance, G-metric, modular metric, probabilistic metric, fuzzy metric, graphical metric and corresponding fixed point theory but also motivates work on existing open problems on the subject. Each of the nine chapters—contributed by various authors—contains an Introduction section which summarizes the material needed to read the chapter independently of the others and contains the necessary background, several examples, and comprehensive literature to comprehend the concepts presented therein. This is helpful for those who want to pursue their research career in metric fixed point theory and its related areas. Features Explores the latest research and developments in fixed point theory on the most popular generalizations of metric spaces Description of various generalizations of metric spaces Very new topics on fixed point theory in graphical and modular metric spaces Enriched with examples and open problems This book serves as a reference for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed points. It may also be used as a text book for postgraduate and research students who are trying to derive future research scope in this area.
| Author | : Erdal Karapinar |
| Publisher | : Springer Nature |
| Total Pages | : 141 |
| Release | : 2022-12-07 |
| Genre | : Mathematics |
| ISBN | : 3031149696 |
Download Fixed Point Theory in Generalized Metric Spaces Book in PDF, ePub and Kindle
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
| Author | : Yeol Je Cho |
| Publisher | : Nova Publishers |
| Total Pages | : 222 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9781594548734 |
Download Fixed Point Theory and Applications, Volume 6 Book in PDF, ePub and Kindle
Fixed Point Theory & Applications
| Author | : Vittorino Pata |
| Publisher | : Springer Nature |
| Total Pages | : 171 |
| Release | : 2019-09-22 |
| Genre | : Mathematics |
| ISBN | : 3030196704 |
Download Fixed Point Theorems and Applications Book in PDF, ePub and Kindle
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.
