In this paper we deal with set-valued maps T:X⇉X⁎ defined on a Banach space X, that are generalized monotone in the sense of Karamardian. Under various continuity assumptions on T, we investigate the regularity of suitable selections of the set-valued map R++T that shares with T the generalized monotonicity properties. In particular, we show that for every quasimonotone set-valued map T satisfying the Aubin property around (y,y⁎)∈gph(T) with y⁎≠0 there exist locally Lipschitz selections of R++T∖{0}. In the last part some notions of Minty points of T are introduced, and their relationship with zeros as well as effective zeros of T is discussed; a correlation is established between these concepts and the broader context of the generalized monotonicity of the map T.

Bianchi, M., Hadjisavvas, N., Pini, R. (2024). On the regularity of selections and on Minty points of generalized monotone set-valued maps. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 535(2 (15 July 2024)) [10.1016/j.jmaa.2024.128234].

On the regularity of selections and on Minty points of generalized monotone set-valued maps

Pini, R
2024

Abstract

In this paper we deal with set-valued maps T:X⇉X⁎ defined on a Banach space X, that are generalized monotone in the sense of Karamardian. Under various continuity assumptions on T, we investigate the regularity of suitable selections of the set-valued map R++T that shares with T the generalized monotonicity properties. In particular, we show that for every quasimonotone set-valued map T satisfying the Aubin property around (y,y⁎)∈gph(T) with y⁎≠0 there exist locally Lipschitz selections of R++T∖{0}. In the last part some notions of Minty points of T are introduced, and their relationship with zeros as well as effective zeros of T is discussed; a correlation is established between these concepts and the broader context of the generalized monotonicity of the map T.
Articolo in rivista - Articolo scientifico
Aubin property; Minty points; Pseudomonotone set-valued map; Quasimonotone set-valued map; Selections; Sign-continuity;
English
20-feb-2024
2024
535
2 (15 July 2024)
128234
embargoed_20260220
Bianchi, M., Hadjisavvas, N., Pini, R. (2024). On the regularity of selections and on Minty points of generalized monotone set-valued maps. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 535(2 (15 July 2024)) [10.1016/j.jmaa.2024.128234].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/461835
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