1 citations · 1 across the 5 of their papers we have counts for
5 papers
Validity of the Strong Version of the Union of Uniform Closed Balls Conjecture in the Plane
Chadi Nour, Jean Takche
We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.
New Characterizations of Strong Convexity
Chadi Nour, Jean Takche
Parallel to the main results of [13] and [14], which explore the equivalence between prox-regularity, the exterior sphere condition, and -convexity, we present novel characteriz…
The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We provide a novel analytical proof of an improved version of [10, Theorem 3.1], showing that the complement of a closed set satisfying the extended exterior sphere condition is no…
The Variable Radius Form of the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothin…
The Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We prove that the complement of a closed set S satisfying an extended exterior sphere condition is nothing but the union of closed balls with common radius. This generalizes [11, T…