Minimax Theory and its Applications 09 (2024), No. 2, 201--224
Copyright Heldermann Verlag 2024
Inheritance Properties on Cone Continuity for Set-Valued Maps via Scalarization
Premyuda Dechboon
Graduate School of Science and Technology, Niigata University, Niigata, Japan
dechboon@m.sc.niigata-u.ac.jp
Tamaki Tanaka
Faculty of Science, Niigata University, Niigata, Japan
tamaki@math.sc.niigata-u.ac.jp
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.
Keywords: Set optimization, set relation, set-valued map, scalarization function, semicontinuity, cone continuity, preorder semicontinuity.
MSC: 49J53, 49J45, 54C60, 46N10.
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