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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Finite-dimensional Banach spaces with a.e. differentiable metric projection


Author: Theagenis Abatzoglou
Journal: Proc. Amer. Math. Soc. 78 (1980), 492-496
MSC: Primary 41A50; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1980-0556619-8
MathSciNet review: 556619
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Abstract: We prove that in a finite-dimensional Banach space, where the Hessian of the norm square is positive definite on the whole space, except possibly at 0, the metric projection onto any closed set is differentiable a.e.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0556619-8
Article copyright: © Copyright 1980 American Mathematical Society