Fixed Point Theory in Distance Spaces

Name: Fixed Point Theory in Distance Spaces
Brand: Springer International Publishing AG
SKU: 9783319364056
Price: 216.95 PLN
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Autor: William Kirk, Naseer Shahzad

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Oprawa: Miękka

Wydawca: Springer International Publishing AG

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This is a monograph on fixed point theory, covering the purely metric aspects of the theory-particul...

Informacje o książce

Autor

William Kirk, Naseer Shahzad

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2016

strony

173

EAN

9783319364056

ISBN

3319364057

Enbook ID

13633584

Wydawca

Springer International Publishing AG

Waga

2934

Wymiary

155 x 235 x 237

Pełny opis

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.

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