Concave function inequality
Video created by National Research University Higher School of Economics for the course "Mathematics for economists". Week 6 of the Course is devoted to ... ,In mathematics, a concave function is the negative of a convex function. A concave function is ... See also[edit]. Concave polygon · Jensen's inequality · Logarithmically concave function · Quasiconcave function · Concavifi,In mathematics, a real-valued function defined on an n-dimensional interval is called convex if ... This result, known as Jensen's inequality, can be used to deduce inequalities such as the arithmetic–geometric mean ... Likewise, a "concave",A general property of concavity is for x1<x2<x3. f(x2)−f(x1)x2−x1⩾f(x3)−f(x1)x3−x1⩾f(x3)−f(x2)x3−x2. This can be proved from the basic ... , ,In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, ... while the graph of the function is the convex function of the weighted means,. f ( t x 1 + ( 1 − t ) x 2 ) . ... is concave, which is. φ ( ∑ a i x i ∑ a i )&nb,Jensen's Inequality. Theorem. For any concave function f,. E[f(X)] ≤ f(E[X]). Proof. Suppose f is differentiable. The function f is concave if, for any x and y,. ,A concave function: no line segment joining two points on the graph lies above ... Jensen's inequality: another characterization of concave and convex functions. ,If the reversed inequality in (1.1) holds, then f is concave. If [ a , b ] ⊆ I , then the following double inequality holds for any convex function f : (1.2) f ( a + b 2 ) ≤ 1 ... ,Recall first Favard's inequality [5, p. 41 I] which states that where. J'is a nonnegative concave function on [0, I] and .f = i'l f(x) d.Y. '0 then, for each #, convex on [0, ...
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 Concave function inequality 相關參考資料
6.9. Inequality for concave function in n-dimensional space ...
Video created by National Research University Higher School of Economics for the course "Mathematics for economists". Week 6 of the Course is devoted to ... https://www.coursera.org Concave function - Wikipedia
In mathematics, a concave function is the negative of a convex function. A concave function is ... See also[edit]. Concave polygon · Jensen's inequality · Logarithmically concave fun... https://en.wikipedia.org Convex function - Wikipedia
In mathematics, a real-valued function defined on an n-dimensional interval is called convex if ... This result, known as Jensen's inequality, can be used to deduce inequalities such as the arithm... https://en.wikipedia.org Inequality for concave function - Mathematics Stack Exchange
A general property of concavity is for x1<x2<x3. f(x2)−f(x1)x2−x1⩾f(x3)−f(x1)x3−x1⩾f(x3)−f(x2)x3−x2. This can be proved from the basic ... https://math.stackexchange.com Jensen's Inequality
https://www.probabilitycourse. Jensen's inequality - Wikipedia
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, ... while the graph of the function is the convex function of the weighted means,. f ( t x 1 + ( 1 − t ) x 2... https://en.wikipedia.org Jensen's Inequality Theorem For any concave function f, E[f(X ...
Jensen's Inequality. Theorem. For any concave function f,. E[f(X)] ≤ f(E[X]). Proof. Suppose f is differentiable. The function f is concave if, for any x and y,. http://www.sef.hku.hk Mathematical methods for economic theory: 3.1 Concave and ...
A concave function: no line segment joining two points on the graph lies above ... Jensen's inequality: another characterization of concave and convex functions. https://mjo.osborne.economics. On some inequalities for h-concave functions - ScienceDirect
If the reversed inequality in (1.1) holds, then f is concave. If [ a , b ] ⊆ I , then the following double inequality holds for any convex function f : (1.2) f ( a + b 2 ) ≤ 1 ... https://www.sciencedirect.com Some Inequalities for Generalized Concave Functions - Core
Recall first Favard's inequality [5, p. 41 I] which states that where. J'is a nonnegative concave function on [0, I] and .f = i'l f(x) d.Y. '0 then, for each #, convex on [0, ... ... https://core.ac.uk |