Geometric Properties of Banach Spaces and Nonlinear by Charles Chidume

By Charles Chidume

The contents of this monograph fall in the basic quarter of nonlinear sensible research and functions. We specialize in an immense subject inside of this sector: geometric homes of Banach areas and nonlinear iterations, a subject of in depth examine e?orts, in particular in the prior 30 years, or so. during this conception, a few geometric houses of Banach areas play an important function. within the ?rst a part of the monograph, we disclose those geometric homes such a lot of that are popular. As is celebrated, between all in?nite dim- sional Banach areas, Hilbert areas have the nicest geometric homes. the supply of the internal product, the truth that the proximity map or nearest aspect map of a true Hilbert area H onto a closed convex subset okay of H is Lipschitzian with consistent 1, and the next 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 carry for all x,y? H, are a number of the geometric houses that char- terize internal product areas and likewise determine difficulties posed in Hilbert areas extra potential than these regularly Banach areas. despite the fact that, as has been rightly saw by means of M. Hazewinkel, “... many, and doubtless so much, mathematical items and versions don't evidently reside in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach areas, analogues of the identities (?) and (??) must be developed.

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

The contents of this monograph fall in the common sector of nonlinear useful research and purposes. We concentrate on a major subject inside of this region: geometric homes of Banach areas and nonlinear iterations, a subject matter of in depth learn e? orts, in particular in the earlier 30 years, or so.

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