Topology and approximate fixed points / Afif Ben Amar, Donal O'Regan.
2022
QA329.9
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Title
Topology and approximate fixed points / Afif Ben Amar, Donal O'Regan.
Author
Ben Amar, Afif, author.
ISBN
9783030922047 (electronic bk.)
3030922049 (electronic bk.)
3030922030
9783030922030
3030922049 (electronic bk.)
3030922030
9783030922030
Publication Details
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-92204-7 doi
Call Number
QA329.9
Dewey Decimal Classification
515/.7248
Summary
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces and fundamental properties of their topologies are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 3, 2022).
Added Author
O'Regan, Donal, author.
Series
Developments in mathematics ; v. 71. 2197-795X
Available in Other Form
Print version: 9783030922030
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Table of Contents
Preface
Basic Concepts
Almost Fixed Points
Approximate Fixed Points in Ultrametric Spaces
Synthetic Approaches to Problems of Fixed Points
Approximate Fixed Theory in Topological Vector Spaces
Bibliography.
Basic Concepts
Almost Fixed Points
Approximate Fixed Points in Ultrametric Spaces
Synthetic Approaches to Problems of Fixed Points
Approximate Fixed Theory in Topological Vector Spaces
Bibliography.