Topology and Approximate Fixed Points

Afif Ben Amar author Donal O'Regan author

Format:Paperback

Publisher:Springer Nature Switzerland AG

Published:27th Jan '23

Currently unavailable, and unfortunately no date known when it will be back

This paperback is available in another edition too:

Topology and Approximate Fixed Points cover

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 areweak 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 pointtheory.

“The book is very well written, with accurate and detailed arguments in the proofs and inspiring interpretations of the statements of the results. This book is a valuable resource for graduate students who wish to learn about advanced topology and fixed point theory but it will also be useful to researchers in the area.” (Jarosław Górnicki, zbMATH 1492.54018, 2022)
“The book is very well written, with accurate and detailed arguments in the proofs and inspiring interpretations of the statements of the results. This book is a valuable resource for graduate students who wish to learn about advanced topology and fixed point theory but it will also be useful to researchers in the area.” (Jarosław Górnicki, zbMATH 1492.54018, 2022)

ISBN: 9783030922061

Dimensions: unknown

Weight: unknown

251 pages

1st ed. 2022