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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.

Fixed point theory. --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics)

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Fixed point theory. --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Extremal problems

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Mathematics --- Fixed point theory --- Théorème du point fixe --- Periodicals. --- Périodiques --- Point fixe, Théorème du --- Mathematical Sciences --- Applied Mathematics --- Fixed point theory. --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics)

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Presents the trends in topological fixed point theory. This book is useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems.

Fixed point theory --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Differential Equations. --- Differential equations, partial. --- Algebraic topology. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Algebraic Topology. --- Topology --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Differential equations. --- Partial differential equations.

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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.

Fixed point theory. --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Global differential geometry. --- Topology. --- Differential Geometry. --- Mathematical Modeling and Industrial Mathematics. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry, Differential --- Differential geometry. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Differential geometry