scholarly journals ON A SEPARATION THEOREM INVOLVING THE QUASI-RELATIVE INTERIOR

2007 ◽  
Vol 50 (3) ◽  
pp. 605-610 ◽  
Author(s):  
F. Cammaroto ◽  
B. Di Bella
Keyword(s):  
Separation Theorem ◽  
Relative Interior ◽  
Separation Theorems ◽  
Quasi Relative Interior

AbstractWe establish two separation theorems in which the classic interior is replaced by the quasi-relative interior.

Regularity Conditions via Quasi-Relative Interior in Convex Programming

2008 ◽  
Vol 19 (1) ◽  
pp. 217-233 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Gert Wanka
Keyword(s):  
Convex Programming ◽  
Relative Interior ◽  
Regularity Conditions ◽  
Quasi Relative Interior

scholarly journals Existence Theorems for Vector Equilibrium Problems via Quasi-Relative Interior

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Capătă Adela Elisabeta
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Relative Interior ◽  
Vector Equilibrium Problems ◽  
Quasi Relative Interior ◽  
Vector Equilibrium ◽  
Convexity Assumptions

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

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