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Fixed point property under renormings in non-reflexive Banach spaces


Marketed By :  LAP LAMBERT Academic Publishing   Sold By :  Kamal Books International  
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  • Product Description

Consider a subset C of a Banach space (X,||·||). Let T be a mapping from a set C to itself, it is said that a point x in C is a fixed point for T if Tx=x. This mapping is a nonexpansive mapping if ||Tx - Ty||?||x - y|| for all x and y belonging to C. It is said that a Banach space X has the fixed point property (FPP) if every nonexpansive mapping defined from a closed convex bounded subset into itself has a fixed point. For a long time, it was conjectured that all Banach spaces with the FPP had to be reflexive. In 2008, it was given an unexpected answer to this conjecture: it was found the first known nonreflexive Banach space with the FPP. On the other hand, in 2009, it was proved that every reflexive Banach space can be renormed to have the FPP. This leads us to the following question: Which type of nonreflexive Banach spaces can be renormed to have the FPP? So, the main object of this book is to study new families of nonreflexive Banach spaces which can be renormed to have the FPP.

Product Specifications
SKU :COC24269
AuthorCarlos Alberto Hernández Linares and María Ángeles Japón Pineda
Number of Pages112
Publishing Year7/30/2012
Edition1 st
Book TypeReal analysis, real variables
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-28 00:00:00