1 citations · 2 across the 7 of their papers we have counts for
7 papers
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…
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…
Relationships between Global and Local Monotonicity of Operators
Pham Duy Khanh, Vu Vinh Huy Khoa, Juan Enrique Martínez-Legaz +1
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between fi…
Closed convex sets of Motzkin and generalized Minkowski types
Juan Enrique Martínez-Legaz, Cornel Pintea
The aim of this paper is twofold. On one hand the generalized Minkowski sets are defined and characterized. On the other hand, the Motzkin decomposable sets, along with their epigr…
Fenchel subdifferential operators: a characterization without cyclic monotonicity
Juan Enrique Martínez-Legaz
Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclical…
Co-radiant set-valued mappings
Abelardo Jordán, Juan Enrique Martínez-Legaz
We introduce and study a notion of co-radiantness for set-valued mappings between nonnegative orthants of Euclidean spaces. We analyze them from an abstract convexity perspective.…
Characterization of Lipschitz continuous DC functions
A. Hantoute, J. E. Martínez-Legaz
We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a locally convex space, to be Lipschitz continuous. Our criterion reli…