WebMar 6, 2024 · A subset [math]\displaystyle{ S }[/math] of a real or complex vector space [math]\displaystyle{ X }[/math] is called a disk and is said to be disked, absolutely convex, and convex balanced if any of the following equivalent conditions is satisfied: [math]\displaystyle{ S }[/math] is a convex and balanced set. WebConvex functions are real valued functions which visually can be understood as functions which satisfy the fact that the line segment joining any two points on the graph of the function lie above that of the function. Some familiar examples include x \mapsto x^2 x ↦ x2, x \mapsto e^x x ↦ ex, etc. Source: Wikipedia: Eli Osherovich.
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In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonn… WebOct 23, 2024 · Convex set. in a Euclidean or in another vector space. A set containing with two arbitrary points all points of the segment connecting these points. The intersection of any family of convex sets is itself a convex set. The smallest dimension of a plane (i.e. affine subspace) containing a given convex set is called the dimension of that set. how to solve math word problems algebra
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WebNov 10, 2024 · Applying this, the set V is closed because it is the intersection of pre-images of the closed set [logy, ∞) under the continuous functions (x1, x2) ↦ ax1 and (x1, x2) ↦ bx2. As far as convexity goes, your approach is almost correct. Let t(x1, x2) + (1 − t)(x ′ 1, x ′ 2) = (tx1 + (1 − t)x ′ 1, tx2 + (1 − t)x2) be an element of ... WebFeb 7, 2011 · Convex analysis. A branch of mathematics occupying a place intermediate between analysis and geometry, the subject of which are convex functions, convex functionals and convex sets (cf. Convex function (of a real variable); Convex functional; Convex set ). The foundations of convex analysis were laid by H. Minkowski [1], [2], … WebOct 23, 2024 · Convex set. in a Euclidean or in another vector space. A set containing with two arbitrary points all points of the segment connecting these points. The intersection of … novel cool pokemon sword and shield