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    STUDIA MATHEMATICA - Issue no. 4 / 2009  
         
  Article:   BOOK REVIEWS: CHARLES CHIDUME, GEOMETRIC PROPERTIES OF BANACH SPACES AND NONLINEAR ITERATIONS, LECTURES NOTES IN MATHEMATICS, VOL. 1965, SPRINGER-VERLAG LONDON LIMITED, 2009, XVII+326 PP; ISBN: 978-1-84882-189-7, E-ISBN: 978-1-8488.

Authors:  ŞTEFAN COBZAŞ. 		 
       
         
  Abstract:  The aim of the present book is to give an introduction to this very active area of investigation. The basic results from the geometry of Banach spaces are presented in the first five chapters of the book: 1. Some geometric properties of Banach spaces, 2. Smooth spaces, 3. Duality map in Banach spaces, 4. Inequalities in uniformly convex spaces, and 5. Inequalities in uniformly smooth spaces. The study of iterative procedures starts in Chapter 6. Iterative methods for fixed points of nonexpansive mappings, and continues along the rest of the chapters (there are 23) with topics as: descent methods for variational inequalities (in Ch. 7), iterative procedures for zeros of generalized accretive operators (Chapters 8 and 9), iterations for pseudo-contractive mappings (Chapters 10 to 12), iterative methods for generalized nonexpansive mappings (Ch. 14), for families of nonexpansive mappings (Chapters 15 to 17), for asymptotically nonexpansive mappings (Chapters 20 and 21) and for nonexpansive semigroups (Ch. 22).  
         
     
         
         
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