Topology and Approximate Fixed Points (Developments in Mathematics, 71) free ebook download.

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Topology and Approximate Fixed Points (Developments in Mathematics, 71) free ebook download

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Author(s):	Afif Ben Amar

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	3030922030
Pages:	264	OCR:		Quality:		ISBN13:
Uploader:	risotor	Upload Date:	1/25/2024 8:31:14 PM

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3030922030 pdf
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 spacesand fundamental properties of their topologiesare 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 Frchet-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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Tags: Approximate Developments Fixed Mathematics Points Topology

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