Geometric Properties of Banach Spaces and Nonlinear Iterations - Couverture souple

Chidume, Charles

Couverture souple

ISBN 10 : 1848821891 ISBN 13 : 9781848821897

Editeur : Springer, 2009

Synopsis

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

A propos du livre

Présentation de l'éditeur

This text is a comprehensive and up-to-date look at geometric properties of Banach spaces and nonlinear iterations. Recent years have seen an explosion of research and papers in this field, and this text incorporates all the new information.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 1848821891
• ISBN 13: 9781848821897
• Reliure: Broché
• Nombre de pages: 352
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne