Geodesic
Inheritance Properties on Cone Continuity for Set-Valued Maps via Scalarization
Minimax theory and its applications, Tome 9 (2024) no. 2

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This paper unravels the mechanism by which composite functions of a set-valued map and a scalarization function inherit semicontinuity of parent set-valued maps through several scalarization for sets. Consequently, almost all results given by Sonda, Kuwano and Tanaka in 2010 are verified in general settings where we generalize both concepts of cone-continuity for set-valued maps and ordinary lower and upper semicontinuities for real-valued functions
Mots-clés : Set optimization, set relation, set-valued map, scalarization function, semicontinuity, cone continuity,-semicontinuity 
Premyuda Dechboon,Tamaki Tanaka. Inheritance Properties on Cone Continuity for Set-Valued Maps via Scalarization. Minimax theory and its applications, Tome 9 (2024) no. 2. http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a3/
@article{MTA_2024_9_2_a3,
     author = {Premyuda Dechboon,Tamaki Tanaka},
     title = {Inheritance {Properties} on {Cone} {Continuity} for {Set-Valued} {Maps} via {Scalarization}},
     journal = {Minimax theory and its applications},
     year = {2024},
     volume = {9},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a3/}
}
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