Geodesic
The Lipschitz Condition of the Metric Projection in the Plis Metric
Journal of convex analysis, Tome 27 (2020) no. 3, pp. 923-934
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We consider the class of Banach spaces where the metric projection on a convex closed bounded set is Lipschitz continuous in the Plis metric with respect to the set. We obtain some geometrical and analytical conditions for this property. In fact, the space should has a Hilbert-like structure.
Classification : 49J53, 52A07, 46C05, 26B25, 46B25, 46B20
Mots-clés : Uniform convexity, uniform smoothness, Banach space, Hilbert space, metric projection, Plis metric, moduli of convexity and smoothness 
@article{JCA_2020_27_3_JCA_2020_27_3_a6,
     author = {M. V. Balashov},
     title = {The {Lipschitz} {Condition} of the {Metric} {Projection} in the {Plis} {Metric}},
     journal = {Journal of convex analysis},
     pages = {923--934},
     year = {2020},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a6/}
}
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M. V. Balashov. The Lipschitz Condition of the Metric Projection in the Plis Metric. Journal of convex analysis, Tome 27 (2020) no. 3, pp. 923-934. http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a6/