Characterizations of the set containment with star-shaped constraints

Document Type: Research Paper

Authors

1 Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

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.

Keywords

International Journal of Nonlinear Analysis and Applications

Articles in Press, Accepted Manuscript
Available Online from 26 December 2018

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