Semicontinuity of the composition of set-valued map and scalarization function for sets

Abstract

In this paper, we deal with the inheritation of the semicontinuity of set-valued maps via general scalarization for sets, which is regarded as the framework of generalizations of results by Kuwano, Tanaka, and Yamada in 2010. Since the unified scalarization functions for sets satisfy certain desired semicontinuity, our main theorems can be reduced to the results in earlier study.