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Geometrical methods of nonlinear analysis. Transl. from the Russian by Christian C. Fenske. (English) Zbl 0546.47030
Grundlehren der Mathematischen Wissenschaften, 263. Berlin etc.: Springer-Verlag. xix, 409 p. DM 138.00; $ 51.50 (1984).
This is a careful translation of the Russian original (for a detailed review see Zbl 0326.47052) which has merit from several viewpoints. The translator has not only eliminated some inaccuracies, but also collected all references (whose part was scattered in several footnotes in the Russian original) at the end of the book. An additional list of symbols (lacking in the original version) is particularly helpful. Without any doubt this book will become now a world-wide standard reference in nonlinear analysis.
Reviewer: Jürgen Appell

47J05 Equations involving nonlinear operators (general)
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
55M25 Degree, winding number
58C30 Fixed-point theorems on manifolds
54H25 Fixed-point and coincidence theorems (topological aspects)