Topology and Approximate Fixed Points

Name: Topology and Approximate Fixed Points
SKU: 978-3-030-92206-1
Price: 181.70 CHF
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Autor/en: Afif Ben Amar

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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.

ISBN: 978-3-030-92206-1

GTIN: 9783030922061

Autor	Ben Amar, Afif / O'Regan, Donal
Verlag	Springer
Einband	Kartonierter Einband (Kt)
Erscheinungsjahr	2023
Seitenangabe	268 S.
Ausgabekennzeichen	Englisch
Masse	H23.5 cm x B15.5 cm x D1.5 cm 411 g

Über den Autor Afif Ben Amar

Donal O'Regan is 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 is the author of several books, including An Introduction to Ordinary Differential Equations (with Ravi Agarwal), and Oscillation and Stability of Delay Models in Biology (with Ravi Agarwal and Samir Saker). His articles have appeared in journals such as Positivity, Boundary Value Problems, and Fixed Point Theory and Applications. Afif Ben Amar is Professor in the Department of Mathematics, Faculty of Sciences, at the University Sfax, Tunisia. His research interests include operator theory, partial differential equations, integral equations, and applications of mathematics to the natural sciences. His work has been featured in the Arabian Journal of Mathematics, Afrika Mathematika, and Acta Applicandae Mathematicae.