Weak compactness and fixed point property for affine bi-Lipschitz maps

Let X be a Banach space and let C closed convex bounded subset of . It is proved that weakly compact if, only has the generic fixed point property ( G -FPP) for class L -bi-Lipschitz affine mappings every > 1 also if Pełczyński's u ), then either compact, contains an ℓ -sequence or c 0 -summing basic sequence. In this case, weak compactness equivalent to -FPP strengthened are uniformly bi-Lipschitz. We introduce generalized form called su ) , use it prove wide-( s sequence which shift equivalent. in such spaces can characterized terms bi-Lipschitz mappings. with spreading basis thus stronger than ). These results yield significant strengthening important theorem Benavides, Japón-Pineda Prus published 2004.