Convex Definition
 kŏnvĕks, kən-vĕks 
    adjective
  
 Curving outward like the surface of a sphere.
 Webster's New World 
(mathematics, not comparable, of a set) Arranged such that for any two points in the set, a straight line between the two points is contained within the set.
 Wiktionary 
(functional analysis, not comparable, of a real-valued function on the reals) Having an epigraph which is a convex set.
Wiktionary 
    noun
  
 A convex surface, line, object, etc.
 Webster's New World 
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