Libro Fixed Point Theory in Distance Spaces De Kirk, William ; Shahzad, Naseer

portada Fixed Point Theory in Distance Spaces

Formato

Libro Físico

Autor

William Kirk

Naseer Shahzad

Editorial

Springer

Idioma

Inglés

N° páginas

173

Encuadernación

Tapa Dura

Dimensiones

23.4 x 15.6 x 1.3 cm

Peso

0.44 kg.

ISBN13

9783319109268

Categorías

Geometría diferencial y riemanniana
Topología
Modelos y simulaciones por ordenador

Fixed Point Theory in Distance Spaces

William Kirk (Autor) · Naseer Shahzad (Autor) · Springer · Tapa Dura

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Reseña del libro "Fixed Point Theory in Distance Spaces"

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.