Geometric Properties of Banach Spaces and Nonlinear Iterations

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Geometric Properties of Banach Spaces and Nonlinear Iterations (Lecture Notes in Mathematics, 1965)
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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, â€œ... many, and probably most, mathematical objects and models do not naturally live in Hilbert spacesâ€. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
Country USA
Brand Springer
Manufacturer Springer
Binding Paperback
ItemPartNumber biography
ReleaseDate 2009-03-26
UnitCount 1
EANs 9781848821897

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Paperback
ItemPartNumber	biography
ReleaseDate	2009-03-26
UnitCount	1
EANs	9781848821897

Geometric Properties of Banach Spaces and Nonlinear Iterations (Lecture Notes in Mathematics, 1965)

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