Topology and Approximate Fixed Points
janv. 2022 · Developments in Mathematics Livre 71 · Springer Nature
E-book
251
Pages
reportLes notes et avis ne sont pas vérifiés. En savoir plus
À propos de cet e-book
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.
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.
À propos de l'auteur
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).
Donner une note à cet e-book
Dites-nous ce que vous en pensez.
Informations sur la lecture
Smartphones et tablettes
Installez l'application Google Play Livres pour Android et iPad ou iPhone. Elle se synchronise automatiquement avec votre compte et vous permet de lire des livres en ligne ou hors connexion, où que vous soyez.
Ordinateurs portables et de bureau
Vous pouvez écouter les livres audio achetés sur Google Play à l'aide du navigateur Web de votre ordinateur.
Liseuses et autres appareils
Pour lire sur des appareils e-Ink, comme les liseuses Kobo, vous devez télécharger un fichier et le transférer sur l'appareil en question. Suivez les instructions détaillées du Centre d'aide pour transférer les fichiers sur les liseuses compatibles.
