Description: Fixed Point Theory in Distance Spaces Please note: this item is printed on demand and will take extra time before it can be dispatched to you (up to 20 working days). Author(s): William Kirk, Naseer Shahzad Format: Paperback Publisher: Springer International Publishing AG, Switzerland Imprint: Springer International Publishing AG ISBN-13: 9783319364056, 978-3319364056 Synopsis 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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Book Title: Fixed Point Theory in Distance Spaces
Number of Pages: 173 Pages
Publication Name: Fixed Point Theory in Distance Spaces
Language: English
Publisher: Springer International Publishing A&G
Item Height: 235 mm
Subject: Engineering & Technology, Mathematics
Publication Year: 2016
Type: Textbook
Item Weight: 2934 g
Author: Naseer Shahzad, William Kirk
Item Width: 155 mm
Format: Paperback
