Convex
101Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …
102Orthogonal convex hull — The orthogonal convex hull of a point set In Euclidean geometry, a set is defined to be orthogonally convex if, for every line L that is parallel to one of the axes of the Cartesian coordinate system, the intersection of K with L is empty, a… …
103Dynamic convex hull — The dynamic convex hull problem is a class of dynamic problems in computational geometry. The problem consists in the maintenance, i.e., keeping track, of the convex hull for the dynamically changing input data, i.e., when input data elements may …
104Proper convex function — In mathematics, a proper convex function is a convex function f taking values in the extended real number line such that:f(x) < +inftyfor at least one x and :f(x) > inftyfor every x . This definition takes account of the fact that the extended… …
105Logarithmically convex function — In mathematics, a function f defined on an convex subset of a real vector space and taking positive values is said to be logarithmically convex if log f(x) is a convex function of x.It is easy to see that a logarithmically convex function is a… …
106Carathéodory's theorem (convex hull) — See also Carathéodory s theorem for other meanings In convex geometry Carathéodory s theorem states that if a point x of R d lies in the convex hull of a set P , there is a subset P prime; of P consisting of d +1 or fewer points such that x lies… …
107Strictly convex space — In mathematics, a strictly convex space is a normed topological vector space ( V , || ||) for which the unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two points x and y in the boundary ∂… …
108Absolutely convex set — A set C in a real or complex vector space is said to be absolutely convex if it is convex and balanced. Properties A set C is absolutely convex if and only if for any points x 1, , x 2 in C and any numbers lambda 1, , lambda 2 satisfying |lambda… …
109Holomorphically convex hull — In mathematics, more precisely in complex analysis, the holomorphically convex hull of a given compact set in the n dimensional complex space C n is defined as follows. Let G subset {mathbb{C^n be a domain (an open and connected set), or… …
110Schur-convex function — In mathematics, a Schur convex function, also known as S convex, isotonic function and order preserving function is a function f: mathbb{R}^d ightarrow mathbb{R}, for which if forall x,yin mathbb{R}^d where x is majorized by y, then f(x)le f(y).… …
