Topology and Approximate Fixed Points - Afif Ben Amar, Donal O'Regan

Topology and Approximate Fixed Points

Buch | Softcover
XIII, 251 Seiten
2023 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-92206-1 (ISBN)
128,39 inkl. MwSt
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.

lt;b>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.

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.

"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." (Jaroslaw 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)

Erscheinungsdatum
Reihe/Serie Developments in Mathematics
Zusatzinfo XIII, 251 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 385 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte 1_{1}-sequences • approximate fixed point nets • approximate fixed point sequences • Fréchet-Urysohn property • Topological Vector Spaces • ultrametric spaces • weak* topology • Weak topology
ISBN-10 3-030-92206-5 / 3030922065
ISBN-13 978-3-030-92206-1 / 9783030922061
Zustand Neuware
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