Téléchargez le livre : Topology and Approximate Fixed Points

Topology and Approximate Fixed Points



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Springer


Paru le : 2022-01-25



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Description
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.
Pages
251 pages
Collection
n.c
Parution
2022-01-25
Marque
Springer
EAN papier
9783030922030
EAN PDF
9783030922047
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
25
Taille du fichier
2642 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
116,04 €
EAN EPUB
9783030922047
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
25
Taille du fichier
9462 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
116,04 €
Afif Ben Amar is a Professor in the Department of Mathematics, Faculty of Sciences, at the University of Sfax, Tunisia. His research interests lie in operator theory, fixed point theory, nonlinear spectral theory, partial differential equations, integral equations, and applications of mathematics to natural sciences. He co-authored (with Donal O’Regan) the book “Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications”, published by Springer.

Donal O’Regan is a Professor in the School of Mathematics, Statistics, and Applied Mathematics at the National University of Ireland, Galway. His research interests include differential equations, nonlinear analysis, and fixed point theory. He has authored several books, including the Springer titles “Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications (with Afif Ben Amar) and “An Introduction to Ordinary Differential Equations” (with Ravi P. Agarwal).


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