%0 Journal Article
%T Characterizations of the set containment with star-shaped constraints
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Hedayat, Arian
%A Mohebi, Hossein
%D 2021
%\ 02/01/2021
%V 12
%N 1
%P 790-811
%! Characterizations of the set containment with star-shaped constraints
%K star-shaped function
%K co-star-shaped function
%K set containment
%K $nu$-star-shaped-conjugation
%K weak separation
%R 10.22075/ijnaa.2018.13932.1727
%X In this paper, we first give a separation theorem for a closed star-shaped set at the origin and a point outside it in terms of separation by an upper semi-continuous and super-linear function, and also, we introduce a $\nu$-star-shaped-conjugation. By using this facts, we present characterizations of the set containment with infinite star-shaped constraints defined by weak inequalities. Next, we give characterizations of the set containment with infinite evenly radiant constraints defined by strict or weak inequalities. Finally, we give a characterization of the set containment with an upper semi-continuous and radiant constraint, in a reverse star-shaped set, defined by a co-star-shaped constraint. These results have many applications in Mathematical Economics, in particular, in Utility Theory.
%U https://ijnaa.semnan.ac.ir/article_3533_309418436f44ce75503bcaea860db887.pdf