A Hahn-Banach type separation theorem for nonconvex sets

عنوان به زبان ديگر

پديدآورندگان

Karimi Masoud karimi.masoud1984@gmail.com Department of Mathematics, Razi University, Kermanshah, Iran , Kasimbeyli Refail rkasimbeyli@anadolu.edu.tr Department of Industrial Engineering, Anadolu University, Iki Eylul Campus 26470, Eskisehir, Turkey

تعداد صفحه

4

كليدواژه

Nonlinear Separation Theorem , Hahn , Banach Theorem , Bishop , Phelps Cone , Separation Property

سال انتشار

1397

عنوان كنفرانس

چهارمين كنفرانس بين المللي آناليز غير خطي و بهينه سازي

زبان مدرك

انگليسي

چكيده فارسي

The aim of this paper is to present a Hahn-Banach type separation theorem for two disjoint closed sets of Euclidean spaces such that one of them is not necessarily convex. By using the Kasimbeyli’s nonlinear separation theorem from [4] and properties of Bishop-Phelps cones, we first prove a separation theorem for a given closed cone and a point outside from this cone and then we use it to prove separation theorem for two disjoint sets. Illustrative examples are provided to highlight the important aspects of these theorems.

چكيده لاتين

The aim of this paper is to present a Hahn-Banach type separation theorem for two disjoint closed sets of Euclidean spaces such that one of them is not necessarily convex. By using the Kasimbeyli’s nonlinear separation theorem from [4] and properties of Bishop-Phelps cones, we first prove a separation theorem for a given closed cone and a point outside from this cone and then we use it to prove separation theorem for two disjoint sets. Illustrative examples are provided to highlight the important aspects of these theorems.

كشور

ايران