Abstract.
Let X be an infinite-dimensional normed space. We prove the following: There exists a Lipschitz mapping \( \upsilon \) from the unit sphere S(X) into itself without approximate fixed or antipodal points, that is,¶¶ \( \textrm{inf}\, \{\parallel \upsilon(x) \pm x \parallel\, : x \in S(X)\} > 0. \)
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Eingegangen am 31. 1. 2001
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ID="h1"This research was supported by DGES PB 98-1335.
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Jiménez-Vargas, A., Mena-Jurado, J. & Navarro-Pascual, J. Lipschitz mappings on the unit sphere of an infinite-dimensional normed space. Arch. Math. 79, 379–384 (2002). https://doi.org/10.1007/PL00012460
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DOI: https://doi.org/10.1007/PL00012460