Nonstandard Methods in Fixed Point Theory

Authors: A. Aksoy, M.A. Khamsi

Publisher: Springer-Verlag

ISBN: 0387973648

Series: UNIVERSITEXT

Year: 1990.

Reviews:

-- New Technical Books, 1991, USA.

-- Notiziero Della Unione, Mathematica Italiana, 1991, Italy.

-- Optimization, 1991, Germany.

-- Mathematical Reviews, AMS, MR#:91i:47073, 1991, USA.

-- Nonlinear News Book Reviews, 1991, USA.

-- Extrait de l'Enseignement Mathematique, 1990, France.

-- Telegraphic Reviews of the American Monthly, 1991, USA.

Summary:

This book gives a unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for nonexpansive mappings. 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 ultraproduct constructions are studied in detail in the second part, 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 nonexpansive maps in the view of nonstandard methods.