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Nonstandard Methods in Fixed Point Theory

Author: Asuman Güven Aksoy; Mohamed A Khamsi
Publisher: New York, NY : Springer New York, 1990.
Series: Universitext.
Edition/Format:   eBook : Bibliographic data : EnglishView all editions and formats
Summary:
A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic results which follow. Set theoretic and Banach space ultraproducts constructions are studied in detail in the second part of  Read more...
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Details

Genre/Form: Electronic books
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Asuman Güven Aksoy; Mohamed A Khamsi
ISBN: 9781461234449 1461234441
OCLC Number: 840279349
Description: 1 online resource (IX, 139 pages 3 illustrations).
Contents: 0 --
Schauder Bases --
1 --
I. Filters --
II. Limits over Filters --
III.Nets --
2 --
I. The Set-Theoretic Ultraproduct --
II. The Banach Space Ultraproduct --
III. Finite Representability --
IV. Super-(M)-Properties and Banach-Saks Properties --
V. The Ultraproduct of Mappings --
VI. Tzirelson and James Banach Spaces --
3 --
I. An Introduction to Fixed Point Theory --
II. Basic Definitions and Results --
III. Basic Results in Ultraproduct Language --
IV. Some Fixed Point Theorems --
V. Maurey's Theorems --
VI. An Application of Ultranets.
Series Title: Universitext.
Responsibility: by Asuman Güven Aksoy, Mohamed A. Khamsi.

Abstract:

A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic results which follow. Set theoretic and Banach space ultraproducts constructions are studied in detail in the second part of the book, while the remainder of the book gives an introduction to the classical fixed point theory in addition to a discussion of normal structure. This is the first book which studies classical fixed point theory for non-expansive maps in the view of non-standard methods.

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