Topology and approximate fixed points

著者

書誌事項

Topology and approximate fixed points

Afif Ben Amar, Donal O'Regan

(Developments in mathematics, 71)

Springer, c2022

  • hbk.

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注記

Includes bibliographical references (p. 239-246) and index

内容説明・目次

内容説明

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 Frechet-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.

目次

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.

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詳細情報

  • NII書誌ID(NCID)
    BC13873759
  • ISBN
    • 9783030922030
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cham
  • ページ数/冊数
    xiii, 251 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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