Topology and Approximate Fixed Points

Name: Topology and Approximate Fixed Points
Brand: Springer, Berlin
SKU: 9783030922061
Price: 270.51 PLN
Availability: InStock

Autor: Afif Ben Amar, Donal O'Regan

Język:

Oprawa: Miękka

Wydawca: Springer, Berlin

Dostępność: Dostępna u dostawcy

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This book examines in detail approximate fixed point theory in different classes of topological spac...

Informacje o książce

Autor

Afif Ben Amar, Donal O'Regan

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2023

strony

251

EAN

9783030922061

Enbook ID

42688564

Wydawca

Springer, Berlin

Waga

381

Wymiary

155 x 235

Pełny opis

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.

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