Geodesic
An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 196-205

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We construct an example of a three-dimensional strictly convex normed space on which the operator of metric projection onto any straight line does not satisfy the Lipschitz condition.
Keywords: Banach space, metric projection, Chebyshev set, Lipschitz condition. 
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     author = {L. Sh. Burusheva},
     title = {An {Example} of a {Banach} {Space} with {Non-Lipschitzian} {Metric} {Projection} on {Any} {Straight} {Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {196--205},
     publisher = {mathdoc},
     volume = {109},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a3/}
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L. Sh. Burusheva. An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 196-205. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a3/