SMOOTH LIPSCHITZ RETRACTIONS OF STARLIKE BODIES ONTO THEIR BOUNDARIES IN INFINITE-DIMENSIONAL BANACH SPACES
2001 ◽
Vol 33
(4)
◽
pp. 443-453
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Keyword(s):
Let X be an infinite-dimensional Banach space, and let A be a Cp Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that:(1) the boundary ∂A is Cp Lipschitz contractible;(2) there is a Cp Lipschitz retraction from A onto ∂A;(3) there is a Cp Lipschitz map T : A → A with no approximate fixed points.
2005 ◽
Vol 72
(2)
◽
pp. 299-315
◽
1988 ◽
Vol 103
(3)
◽
pp. 497-502
2011 ◽
Vol 53
(3)
◽
pp. 443-449
◽
2020 ◽
Vol 74
(1)
◽
pp. 45