Inheritance Properties on Cone Continuity for Set-Valued Maps via Scalarization
Keywords:
Set optimization, set relation, set-valued map, scalarization function, semicontinuity, cone continuity,-semicontinuityAbstract
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
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