Geometric Properties of Banach Spaces and Nonlinear Iterations (Paperback, 2009 ed.)

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.

General

Imprint:	Springer London
Country of origin:	United Kingdom
Series:	Lecture Notes in Mathematics, 1965
Release date:	March 2009
First published:	2009
Authors:	Charles Chidume
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Paperback
Pages:	326
Edition:	2009 ed.
ISBN-13:	978-1-84882-189-7
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Promotions
LSN:	1-84882-189-1
Barcode:	9781848821897

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