We investigate in the Euclidean framework the behaviour of δ-monotone set-valued maps. This property arises as the natural extension to multivalued maps of the analogous notion enjoyed, for instance, by the gradient of the so-called quasiuniformly convex functions. While on any open subset of the domain the mere property of 5-monotonicity for multivalued maps entails both its single-valuedness and continuity, the behaviour at the boundary points of the domain is, definitely, unpredictable. We consider smooth points of the boundary of the domain, and we show that if a <δ-monotone map is upper semicontinuous, with convex and closed values, then it is single-valued also at those points.

Calogero, A., Pini, R. (2023). A note on δ-monotone maps in Euclidean spaces. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 24(3), 515-525.

A note on δ-monotone maps in Euclidean spaces

Calogero, A;Pini, R
2023

Abstract

We investigate in the Euclidean framework the behaviour of δ-monotone set-valued maps. This property arises as the natural extension to multivalued maps of the analogous notion enjoyed, for instance, by the gradient of the so-called quasiuniformly convex functions. While on any open subset of the domain the mere property of 5-monotonicity for multivalued maps entails both its single-valuedness and continuity, the behaviour at the boundary points of the domain is, definitely, unpredictable. We consider smooth points of the boundary of the domain, and we show that if a <δ-monotone map is upper semicontinuous, with convex and closed values, then it is single-valued also at those points.
Articolo in rivista - Articolo scientifico
5-monotonicity; monotonicity; quasiuniform convexity. ; subdifferential;
English
2023
24
3
515
525
reserved
Calogero, A., Pini, R. (2023). A note on δ-monotone maps in Euclidean spaces. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 24(3), 515-525.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/414431
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