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math.FA2025
On Strongly Convex Sets and Farthest Distance Functions
Juan Enrique Martínez-Legaz
A polarity notion for sets in a Banach space is introduced in such a way that the second polar of a set coincides with the smallest strongly convex set with respect to R that conta…
math.FA2025
A Note on Carlier Inequality
Regina S. Burachik, J. E. Martínez-Legaz
Recently, Carlier established in [3] a quantitave version of the Fitzpatrick inequality in a Hilbert space. We extend this result by Carlier to the framework of reflexive Banach sp…