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Iterative approximation of fixed points. 2nd revised and enlarged ed. (English) Zbl 1165.47047
Lecture Notes in Mathematics 1912. Berlin: Springer (ISBN 978-3-540-72233-5/hbk). xvi, 322 p. EUR 49.95/net; SFR 82.00; $ 74.00; £ 38.50 (2007).

There is a huge amount of existence results for fixed points, very often from a purely theoretical viewpoint, less often more application-oriented. There also exist some survey papers which describe the state of the art of some particular aspects, a prominent example being B. E. Rhoades’ comparison of various definitions of contractive-type maps [Trans. Am. Math. Soc. 226, 257–290 (1977; Zbl 0365.54023)]. However, less is known about specific methods for constructing or approximating fixed points effectively; the present book is intended to fill this gap.

A detailed description of the contents may be found in the review of the first edition (written by B. E. Rhoades) in [(2002; Zbl 1036.47037)]. Specialists in the field will find the list of more than 1500 references particularly useful; thus, this book may also serve as a guide to the literature.

47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47-00Reference works (operator theory)