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Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these mathematical derivations, however, it is worth analyzing an intuitive graphical argument based on the probabilistic case where X is a real number (see figure).
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.
In mathematics, Jensen's theorem may refer to: Johan Jensen's inequality for convex functions; Johan Jensen's formula in complex analysis;
Jensen's formula can be used to estimate the number of zeros of an analytic function in a circle. Namely, if is a function analytic in a disk of radius centered at and if | | is bounded by on the boundary of that disk, then the number of zeros of in a circle of radius < centered at the same point does not exceed
Nvidia CEO Jensen Huang: 'Everybody is counting on us' AT&T CEO on Fed rate cuts: They will make our stock look more attractive Disney investors are glued to CEO succession outcome: Goldman Sachs ...
A continuous, real function on an interval satisfies Jensen's Operator Inequality if the following holds ) (), for operators {} with = and for self ...
Nvidia CEO Jensen Huang anticipates AI will do parts of some jobs 1,000 times better — but it will never replace the actual humans doing those roles. "As we speak, AI has no possibility of doing ...
In an encore “20/20” airing Dec. 27 at 9 p.m. ET, the show, which originally aired in 2023, tells the story of Julie Jensen, the mother of two who was found dead in her bed in 1998.