Strictly convex space information

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...

enclosing a strictly convex set of points Strictly convex set, a set whose interior contains the line between any two points Strictly convex space, a normed...

properties. For instance, a strictly convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional...

In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset...

polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. A strictly convex polygon is a convex polygon...

In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity...

said to be strictly less than an element b, if a ≤ b and a ≠ b . {\displaystyle a\neq b.} For example, { x } {\displaystyle \{x\}} is strictly less than...

\}}} A (strictly) quasiconvex function has (strictly) convex lower contour sets, while a (strictly) quasiconcave function has (strictly) convex upper contour...

{\displaystyle {\log }\circ f} is convex, and Strictly logarithmically convex if log ∘ f {\displaystyle {\log }\circ f} is strictly convex. Here we interpret log...

open half-space uses strict inequality. Half-spaces (open or closed) are affine convex cones. Moreover (in finite dimensions), any convex cone C that...

include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have...

\end{cases}}} The convex conjugate and Legendre transform of the exponential function agree except that the domain of the convex conjugate is strictly larger as...

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"...

a\}} are convex sets. A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically...

does not admit a strictly coarser Hausdorff, locally convex topology. For that reason, the study of sequences begins by finding a strict linear subspace...

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

x_{n}\}}.} The LogSumExp function is convex, and is strictly increasing everywhere in its domain. It is not strictly convex, since it is affine (linear plus...

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

In mathematics, an extreme point of a convex set S {\displaystyle S} in a real or complex vector space is a point in S {\displaystyle S} that does not...

and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same...

concept called strictly decreasing (also decreasing). A function with either property is called strictly monotone. Functions that are strictly monotone are...

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

{5}, {5/2}, and {6}. Beyond Euclidean space, there is an infinite set of regular hyperbolic tilings. The five convex regular polyhedra are called the Platonic...

geodesically convex subset of M. A function f : C → R {\displaystyle f:C\to \mathbf {R} } is said to be a (strictly) geodesically convex function if the...

≤) is replaced by the strict inequality then f {\displaystyle f} is called strictly convex. Convex functions are related to convex sets. Specifically, the...