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

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 {\it B.\,E.\thinspace 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.\thinspace 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.
[Jürgen Appell (Würzburg)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47-00 Reference works (operator theory)

Citations: Zbl 0365.54023; Zbl 1036.47037

Cited in: Zbl 1256.47043 Zbl 1224.54096 Zbl 1217.47118 Zbl 1205.47064 Zbl 1200.47084 Zbl 1173.47052 Zbl 1165.47053 Zbl 1175.47061

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