Nonstandard Methods in Fixed Point Theory (Universitext)

Aksoy, Asuman G.; Khamsi, Mohamed A.

ISBN 10: 0387973648 / ISBN 13: 9780387973647

Editore: Springer, 1990

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Codice articolo SHAK86697

Dati bibliografici

• Titolo: Nonstandard Methods in Fixed Point Theory (Universitext)
• Editore: Springer
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 0387973648
• ISBN 13: 9780387973647
• Rilegatura: Brossura
• Condizione: nuovo

Descrizione articolo

Riassunto

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.

Contenuti

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.