Nonstandard methods in fixed point theory

Asuman G. Aksoy, Mohamed A. Khamsi

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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[目次]

  • 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.- Notes on Normal Structure.- III. Basic Results in Ultraproduct Language.- IV. Some Fixed Point Theorems.- V. Maurey's Theorems.- VI. An Application of Ultranets.

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この本の情報

書名 Nonstandard methods in fixed point theory
著作者等 Aksoy, Asuman G.
Khamsi, Mohamed A
Khamsi Mohamed A.
Aksoy Asuman G.
シリーズ名 Universitext
出版元 Springer-Verlag
刊行年月 c1990
版表示 Softcover reprint of the original 1st ed. 1990
ページ数 ix, 139 p.
大きさ 24 cm
ISBN 3540973648
0387973648
NCID BA10726083
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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