the class of B-convex spaces is a class of Banach space. The concept of B-convexity was defined and used to characterize Banach spaces that have the...

locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They...

convex sets and convex functions is called convex analysis. Spaces in which convex sets are defined include the Euclidean spaces, the affine spaces over...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is...

In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points...

… , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} in a real vector space, a convex combination of these points is a point of the form α 1 x 1 + α 2 x...

n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron"...

locally convex. Other well-known examples of TVSs include Banach spaces, Hilbert spaces and Sobolev spaces. Many topological vector spaces are spaces of functions...

typically not Banach spaces. A Fréchet space X {\displaystyle X} is defined to be a locally convex metrizable topological vector space (TVS) that is complete...

Fundamentals of Convex analysis. Berlin: Springer. Krasnosel'skii M.A., Rutickii Ya.B. (1961). Convex Functions and Orlicz Spaces. Groningen: P.Noordhoff...

define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set...

mathematics, a subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled"...

mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas:...

vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: A + B = { a + b | a ∈ A ,   b ∈ B } {\displaystyle A+B=\{\mathbf...

mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle...

applications in convex minimization, a subdomain of optimization theory. A subset C ⊆ X {\displaystyle C\subseteq X} of some vector space X {\displaystyle...

1981, p. 130. Jarchow, Hans (1981). Locally Convex Spaces. Mathematische Leitfäden. [Mathematical Textbooks]. B. G. Teubner, Stuttgart. ISBN 3-519-02224-9...

compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex subset of a Hausdorff locally convex topological...

it is a barreled space. If X {\displaystyle X} is Hausdorff locally convex TVS then ( X , b ( X , X ′ ) ) {\displaystyle \left(X,b\left(X,X^{\prime }\right)\right)}...

Theorem—Let A {\displaystyle A} and B {\displaystyle B} be non-empty convex subsets of a real locally convex topological vector space X . {\displaystyle X.} If...

convex spaces. Stuttgart: B.G. Teubner. ISBN 978-3-519-02224-4. OCLC 8210342. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces...

a Banach space. A Hausdorff locally convex topological vector space X {\displaystyle X} is normable if and only if its strong dual space X b ′ {\displaystyle...

n-dimensional space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any...

or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach–Steinhaus...

the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is called a star domain (or star-convex set, star-shaped set or radially convex set) if there...

a topological vector space (not necessarily locally convex or Hausdorff) over the real or complex numbers. Then the open convex subsets of X {\displaystyle...

topological vector space (TVS) contains a balanced neighborhood of the origin and every convex neighborhood of the origin contains a balanced convex neighborhood...