Geometric Properties of Banach Spaces and Nonlinear Iterations (Lecture Notes in Mathematics, 1965)
R 1,965
or 4 x payments of R491.25 with
Availability: Currently in Stock
Delivery: 10-20 working days
Condition: USED (All books are in used condition)
Condition - Very Good The item shows wear from consistent use, but it remains in good condition and functions properly. Item may arrive with damaged packaging or be repackaged. It may be marked, have identifying markings on it, or have minor cosmetic damage. It may also be missing some parts/accessories or bundled items.
Geometric Properties of Banach Spaces and Nonlinear Iterations (Lecture Notes in Mathematics, 1965)
Used Book in Good Condition
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 spacesâ€. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.