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Characterizations of the set containment with star-shaped constraints | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 63، دوره 12، شماره 1، مرداد 2021، صفحه 790-811 اصل مقاله (431.06 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.13932.1727 | ||
| نویسندگان | ||
| Arian Hedayat1؛ Hossein Mohebi* 2 | ||
| 1Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran | ||
| 2Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| تاریخ دریافت: 14 بهمن 1396، تاریخ بازنگری: 28 آبان 1397، تاریخ پذیرش: 04 آذر 1397 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| star-shaped function؛ co-star-shaped function؛ set containment؛ $nu$-star-shaped-conjugation؛ weak separation | ||
| مراجع | ||
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